Finite Group Databasebeta

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C3×#69450 #11786393

order1152
isoclinismisoclinic class of #4656
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#69450

Splittings

SylowC32 ⋊ #1851

Subgroups

subgroupG/H
centerC22×C3×C4C22×D3
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×C4×C22⋊C4C2
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC3×C4×C22⋊C4D3
hypocenterC3C3×#1851
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C22⋊C4

777 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, 20404);