Finite Group Databasebeta

C22×C3×#904 #11918603

order1152
isoclinismisoclinic class of #204
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C29

Aliases

direct productC22×C3×#904

Splittings

FittingC23×C32×C8 ⋊ C2
SylowC32 ⋊ C22×#135

Subgroups

subgroupG/H
centerC22×C3×C4D12
commutator, cosocleC3×C4C25×C3
FrattiniC4C24×C3×D3
FittingC23×C32×C8C2
socleC23×C32C2×D4
hypercenterC23×C3×C8D3
hypocenterC3C22×C3×#135
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C23×C3×C4 ◁ C23×C3×C8

3177 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 152614);