Finite Group Databasebeta

C3×#69395 #11790778

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

Aliases

direct productC3×#69395

Splittings

FittingC32×C43 ⋊ C2
SylowC32 ⋊ #1962

Subgroups

subgroupG/H
centerC2×C3×C4C2×D12
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×C43C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#5477C2
cosocleC22×C3×C4C23×C3
hypercenterC3×C43D3
hypocenterC3C3×#1962
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C43

849 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 24789);