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C8×C4⋊(C3⋊Dic3) #11784245

order1152
isoclinismisoclinic class of #634
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C3×C4

Aliases

direct productC8×C4⋊(C3⋊Dic3)

Splittings

SylowC32 ⋊ C8×C4⋊C4

Subgroups

subgroupG/H
centerC22×C8C2×C3⋊D3
commutatorC2×C32C2×C4×C8
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×C4×C8C2
socle, prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenterC2×C4×C8C3⋊D3
hypocenterC32C8×C4⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

888 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1152

Conjugacy classes & character table

336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 18256);