Finite Group Databasebeta

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C3×C4×#823 #11783777

order1152
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×C4×#823

Splittings

FittingC32×C4×M16 ⋊ C2
SylowC32 ⋊ C4×#100

Subgroups

subgroupG/H
centerC2×C3×C4(C2×D3)⋊C4
commutatorC22×C3C2×C3×C42
FrattiniC22×C4C22×C3×D3
FittingC32×C4×M16C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D12C22
cosocleC22×C3×C4C23×C3
hypercenterC3×C4×M16D3
hypocenterC3C3×C4×#100
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×M16

791 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 17788);