Finite Group Databasebeta

C3×C4×#904 #11859983

order1152
isoclinismisoclinic class of #204
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×C4×#904

Splittings

FittingC2×C32×C4×C8 ⋊ C2
SylowC32 ⋊ C4×#135

Subgroups

subgroupG/H
centerC3×C42D12
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4×C8C2
socleC22×C32C22×D4
prime radicalC2×C3×#904C2
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×C4×C8D3
hypocenterC3C3×C4×#135
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C42 ◁ C2×C3×C42 ◁ C2×C3×C4×C8

1081 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 93994);