Finite Group Databasebeta

C3×C4×#907 #11857261

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC3×C4×#907

Splittings

FittingC32×C4×M16 ⋊ C2
SylowC32 ⋊ C4×#131

Subgroups

subgroupG/H
centerC3×C42C22×D3
commutatorC2×C3C22×C3×C42
FrattiniC2×C4C23×C3×D3
FittingC32×C4×M16C2
socleC22×C32C23×C4
prime radicalC2×C3×#235C22
cosocleC2×C3×C4C24×C3
hypercenterC3×C4×M16D3
hypocenterC3C3×C4×#131
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C42 ◁ C3×C4×M16

1215 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, 91272);