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C2×H(5,𝔽2)×C127 #22549591

order8128
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C25×C127 · Schur multiplier (H2) = C29

Aliases

direct productC2×H(5,𝔽2)×C127

Subgroups

subgroupG/H
center, socleC22×C127C24
commutator, Frattini, cosocleC2C25×C127
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ G

898 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4318 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC127×#1790, C127×#1792, C127×#1795, …
maximal normal subgroup ofC127×#1790, C127×#1792, C127×#1795, …
maximal quotient ofC2×#518×C127, C2×#520×C127, C4×H(5,𝔽2)×C127, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8128, 264);