Finite Group Databasebeta

C22×C3×#798 #11899357

order1152
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C23×C3×C8 · Schur multiplier (H2) = C25

Aliases

direct productC22×C3×#798

Splittings

FittingC22×C32×C16 ⋊ C2
SylowC32 ⋊ C22×M32

Subgroups

subgroupG/H
centerC22×C3×C8C2×D3
commutatorC2×C3C23×C3×C8
FrattiniC8C23×C3×D3
FittingC22×C32×C16C2
socleC23×C32C2×C8
prime radicalC23×C3×D3C8
cosocleC3×C8C24×C3
hypercenterC22×C3×C16D3
hypocenterC3C22×C3×M32
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3×C8 ◁ C22×C3×C16

849 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 133368);