Finite Group Databasebeta

C3×#68055 #11777799

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×#68055

Splittings

FittingC32×C82 ⋊ C2
SylowC32 ⋊ #1590

Subgroups

subgroupG/H
centerC2×C3×C4C2×D12
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×C82C2
socleC22×C32C4×D4
prime radicalC2×C3×D12C2×C4
cosocleC3×C42C23×C3
hypercenterC3×C82D3
hypocenterC3C3×#1590
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×C8 ◁ C3×C82

369 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

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, 11810);