Finite Group Databasebeta

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C3×#69461 #11789180

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

Aliases

direct productC3×#69461

Splittings

SylowC32 ⋊ #1921

Subgroups

subgroupG/H
centerC23×C3C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×C4×C4⋊C4C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C3×C4C23×C3
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×#1921
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C3×C4×C4⋊C4

557 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 23191);