The groups of order 128

DOI10.1016/0021-8693(90)90244-IzbMath0694.20011OpenAlexW2033723664MaRDI QIDQ5899695

E. A. O'Brien, M. F. Newman, Rodney James

Publication date: 1990

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(90)90244-i

zbMATH Keywords

automorphism groupsnumber of generatorsisoclinism familiescomputational group theoryCAYLEYpower-commutator presentations\(p\)-covering group\(p\)-group generation algorithm2328 groups of order 128Schur multiplier algorithmTWOGPS

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Finite nilpotent groups, (p)-groups (20D15) Software, source code, etc. for problems pertaining to group theory (20-04)

Related Items (20)

The conjugacy vector of a \(p\)-group of maximal class ⋮ Groups and nilpotent Lie rings whose order is the sixth power of a prime. ⋮ A MILLENNIUM PROJECT: CONSTRUCTING SMALL GROUPS ⋮ On the number of groups of order 1024 ⋮ Unnamed Item ⋮ Birational classification of fields of invariants for groups of order 128 ⋮ Commutators in groups of order p7 ⋮ On endomorphisms of groups of orders 37–47 ⋮ Universal commutator relations, Bogomolov multipliers, and commuting probability ⋮ On 2-groups with submultiplicative spectrum ⋮ CM-fields with relative class number one ⋮ The \(p\)-group generation algorithm ⋮ Finite \(p\)-groups ⋮ Maximal representation dimension of finite p-groups ⋮ On the modular isomorphism problem for groups of class \(3\) and obelisks ⋮ Mod \(2\) group algebras with metabelian unit groups ⋮ Degree three unramified cohomology groups and Noether's problem for groups of order 243 ⋮ The groups with order \(p^7\) for odd prime \(p\). ⋮ The groups of order 256 ⋮ Bogomolov Multipliers of Groups of Order 128

Uses Software

• Cayley

Cites Work

• Computing character degrees in p-groups
• The groups of order dividing 256
• A computer aided classification of certain groups of prime power order
• Determination of the Groups of Orders 101-161, Omitting Order 128
• Determination of the Groups of Orders 162-215 Omitting Order 192
• On Computing the Minimal Number of Defining Relations for Finite Groups
• Minimal presentations for groups of order 2ⁿ, n ≤ 6
• The classification of prime-power groups.
• A Combinatorial Algorithm
• The groups of order 128
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