Finite Group Databasebeta

C3×#78458 #11859473

order1152
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#78458

Splittings

FittingC2×C32×C4×C8 ⋊ C2
SylowC32 ⋊ #2931

Subgroups

subgroupG/H
centerC2×C3×C8C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4×C8C2
socleC22×C32C23×C4
prime radicalC3×#5477C2
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×C4×C8D3
hypocenterC3C3×#2931
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C8 ◁ 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, 93484);