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#585×C127 #22549593

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

Aliases

direct product#585×C127

Subgroups

subgroupG/H
centerC4×C127C24
commutator, Frattini, cosocleC2C25×C127
socleC2×C127C25
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ G

810 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×#1791, C127×#1794, C127×#2901, …
maximal normal subgroup ofC127×#1791, C127×#1794, C127×#2901, …
maximal quotient ofC127×#3428, C4×H(5,𝔽2)×C127, C4×2−1+4×C127, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8128, 266);