Finite Group Databasebeta

C2×C3×#4939 #11801613

order1152
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C3×#4939

Splittings

FittingC22×C32×C42 ⋊ C2
SylowC32 ⋊ C2×#390

Subgroups

subgroupG/H
centerC24×C3C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC22×C32×C42C2
socleC24×C32C23
prime radicalC23×C3×D12C2
cosocleC23×C3C24×C3
hypercenterC22×C3×C42D3
hypocenterC3C2×C3×#390
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C42

2969 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, 35624);