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C4⋊C8×C3⋊Dic3 #11784166

order1152
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C3×C4

Aliases

direct productC4⋊C8×C3⋊Dic3

Splittings

SylowC32 ⋊ C4×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×C3⋊D3
commutatorC2×C32C2×C4×C8
FittingC2×C32×C4⋊C8C2
socle, prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C8C3⋊D3
hypocenterC32C4×C4⋊C8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

948 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, 18177);