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H(5,𝔽2)×C197 #20263229

order6304
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C197 · Schur multiplier (H2) = C25

Aliases

direct productH(5,𝔽2)×C197

Subgroups

subgroupG/H
center, socleC2×C197C24
commutator, Frattini, cosocleC2C24×C197
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C197 ◁ G

166 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3349 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#453×C197, #455×C197, B(4,𝔽2)×C197, …
maximal normal subgroup of#453×C197, #455×C197, B(4,𝔽2)×C197, …
maximal quotient of#518×C197, #520×C197, #534×C197, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6304, 49);