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C22⋊C4×C4⋊(C3⋊D3) #11804752

order1152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C3

Aliases

direct productC22⋊C4×C4⋊(C3⋊D3)

Splittings

FittingC32×C4×C22⋊C4 ⋊ C2
SylowC32 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×C4×C22⋊C4C2
socle, cosocleC23×C32C24
prime radicalC23×C4⋊(C3⋊D3)C2
hypercenterC4×C22⋊C4C3⋊D3
hypocenterC32D4×C22⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C4×C22⋊C4

3756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 38763);