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C4⋊C8×Dic9 #11784165

order1152
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4⋊C8×Dic9

Splittings

SylowC9 ⋊ C4×C4⋊C8

Subgroups

subgroupG/H
centerC22×C4C22×D9
commutatorC2×C9C2×C4×C8
FrattiniC22×C3×C4C22×D3
FittingC2×C9×C4⋊C8C2
socle, prime radicalC23×C3C2×C4×D3
cosocleC22×C4×C9C23
hypercenterC2×C4⋊C8D9
hypocenterC9C4×C4⋊C8
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

474 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1152

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, 18176);