Finite Group Databasebeta

C3×#71679 #11793146

order1152
isoclinismisoclinic class of #69507
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C24

Aliases

direct productC3×#71679

Splittings

SylowC32 ⋊ #2033

Subgroups

subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
Fitting, prime radicalC2×C32×#121C2
socleC23×C32C2×D4
hypercenterC2×C3×#121D3
hypocenterC3C3×#2033
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C2×C3×#121

949 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 27157);