Finite Group Databasebeta

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C3×#67621 #11770895

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

Aliases

direct productC3×#67621

Splittings

SylowC32 ⋊ #1285

Subgroups

subgroupG/H
centerC22×C3C3⋊#95
commutatorC2×C3×C4C3×C42
FrattiniC2×C42C2×C3×D3
FittingC32×C4×C4⋊C4C2
socleC22×C32#95
prime radicalC23×C32C22⋊C4
cosocleC2×C3×C42C22×C3
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×#1285
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×C4×C4⋊C4

425 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 4906);