Finite Group Databasebeta

C3×C4×#893 #11800799

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC3×C4×#893

Splittings

FittingC32×C4×C4⋊C4 ⋊ C2
SylowC32 ⋊ C42×D4

Subgroups

subgroupG/H
centerC22×C3×C4C22×D3
commutatorC2×C3C22×C3×C42
FrattiniC23C23×C3×D3
FittingC32×C4×C4⋊C4C2
socleC23×C32C24
prime radicalC22×C3×D12C22
cosocleC23×C3C24×C3
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×C42×D4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C4⋊C4

1945 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

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, 34810);