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C2×H(5,𝔽2)×C97 #20260450

order6208
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C25×C97 · Schur multiplier (H2) = C29

Aliases

direct productC2×H(5,𝔽2)×C97

Subgroups

subgroupG/H
center, socleC22×C97C24
commutator, Frattini, cosocleC2C25×C97
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C97 ◁ G

898 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3298 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC97×#1790, C97×#1792, C97×#1795, …
maximal normal subgroup ofC97×#1790, C97×#1792, C97×#1795, …
maximal quotient ofC2×#518×C97, C2×#520×C97, C4×H(5,𝔽2)×C97, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6208, 264);