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C4⋊C4×C3⋊(C3⋊C8) #11784251

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

Aliases

direct productC4⋊C4×C3⋊(C3⋊C8)

Splittings

SylowC32 ⋊ C8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×C3⋊D3
commutatorC2×C32C2×C4×C8
FittingC32×C4×C4⋊C4C2
socle, prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenterC4×C4⋊C4C3⋊D3
hypocenterC32C8×C4⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

888 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, 18262);