Finite Group Databasebeta

C3×#68072 #11773645

order1152
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C8

Aliases

direct productC3×#68072

Splittings

FittingC32×#322 ⋊ C2
SylowC32 ⋊ #1453

Subgroups

subgroupG/H
centerC3×C42C22×D3
commutatorC22×C3C2×C3×C42
FrattiniC42C22×C3×D3
FittingC32×#322C2
socleC22×C32C2×C42
prime radicalC22×C3×D3C42
cosocleC3×C42C23×C3
hypercenterC3×#322D3
hypocenterC3C3×#1453
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C3×C42 ◁ C3×#322

413 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 7656);