Finite Group Databasebeta

C3×#70619 #11795077

order1152
isoclinismisoclinic class of #68807
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC3×#70619

Splittings

SylowC32 ⋊ #2083

Subgroups

subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#107C2
socle, prime radicalC23×C32C2×D4
hypercenterC2×C3×#107D3
hypocenterC3C3×#2083
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#107

525 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

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, 29088);