Finite Group Databasebeta

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C4⋊C4×Dic362 #37536636

order23168
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×Dic362

Splittings

SylowC181 ⋊ Q8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D181
commutatorC22×C181C23×C4
FittingC4×C4⋊C4×C181C2
socle, prime radical, cosocleC23×C181C24
hypercenterC4×C4⋊C4D181
hypocenterC181Q8×C4⋊C4
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C23 ◁ C4×C4⋊C4

568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23168

Conjugacy classes & character table

3650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 7425);