Finite Group Databasebeta

C3×#71700 #11792002

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

Aliases

direct productC3×#71700

Splittings

SylowC32 ⋊ #2001

Subgroups

subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C2×D4
prime radicalC24×C32D4
hypercenterC2×C3×C22⋊Q8D3
hypocenterC3C3×#2001
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊Q8

945 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, 26013);