Finite Group Databasebeta

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C22⋊C4×C9⋊C8 #11783635

order1152
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC22⋊C4×C9⋊C8

Splittings

SylowC9 ⋊ C8×C22⋊C4

Subgroups

subgroupG/H
centerC22×C4C22×D9
commutatorC2×C9C2×C4×C8
FrattiniC22×C3×C4C22×D3
FittingC4×C9×C22⋊C4C2
socleC23×C3C22×Dic3
prime radicalC24×C3C2×Dic3
cosocleC22×C4×C9C23
hypercenterC4×C22⋊C4D9
hypocenterC9C8×C22⋊C4
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 17646);