Finite Group Databasebeta

C3×#71973 #11788065

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#71973

Splittings

FittingC23×C32×C8 ⋊ C2
SylowC32 ⋊ #1893

Subgroups

subgroupG/H
centerC23×C3C2×D12
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC23×C32×C8C2
socleC23×C32C2×D4
prime radicalC2×C3×#930C2
cosocleC22×C3×C4C23×C3
hypercenterC23×C3×C8D3
hypocenterC3C3×#1893
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C23×C3×C8

1033 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

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, 22076);