Finite Group Databasebeta

C3×#71432 #11796003

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23

Aliases

direct productC3×#71432

Splittings

FittingC2×C32×M32 ⋊ C2
SylowC32 ⋊ #2113

Subgroups

subgroupG/H
centerC2×C3×C8C22×D3
commutatorC22×C3C22×C3×C8
FrattiniC2×C8C22×C3×D3
FittingC2×C32×M32C2
socleC22×C32C22×C8
prime radicalC2×C3×#235C4
cosocleC2×C3×C8C23×C3
hypercenterC2×C3×M32D3
hypocenterC3C3×#2113
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C8 ◁ C2×C3×M32

501 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

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, 30014);