Finite Group Databasebeta

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C3×#69862 #11775756

order1152
isoclinismisoclinic class of #4451
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×#69862

Splittings

SylowC32 ⋊ #1526

Subgroups

subgroupG/H
centerC2×C3×C4(C2×D3)⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×C4×M16C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC3×C42C23×C3
hypercenterC3×C4×M16D3
hypocenterC3C3×#1526
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×M16

523 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

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, 9767);