Finite Group Databasebeta

← Prev (#11775016) Next (#11775018) →

C3×#71707 #11775017

order1152
isoclinismisoclinic class of #4537
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#71707

Splittings

SylowC32 ⋊ #1501

Subgroups

subgroupG/H
centerC2×C3×C4#217
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
Fitting, prime radicalC32×#525C2
socleC22×C32C2×C22⋊C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#525D3
hypocenterC3C3×#1501
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C3×#525

773 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 9028);