Finite Group Databasebeta

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C22⋊C4×Dic362 #37536556

order23168
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22⋊C4×Dic362

Splittings

SylowC181 ⋊ Q8×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D181
commutatorC22×C181C23×C4
FittingC4×C22⋊C4×C181C2
socle, cosocleC23×C181C24
prime radicalC24×C181C23
hypercenterC4×C22⋊C4D181
hypocenterC181Q8×C22⋊C4
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C23 ◁ C4×C22⋊C4

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11584

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, 7345);