Finite Group Databasebeta

C22×C3×#812 #11899360

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

Aliases

direct productC22×C3×#812

Splittings

SylowC32 ⋊ C22×M32

Subgroups

subgroupG/H
centerC22×C3×C8C2×D3
commutatorC2×C3C23×C3×C8
FrattiniC8C23×C3×D3
FittingC23×C32×C8C2
socleC23×C32C2×C8
prime radicalC24×C32C8
cosocleC3×C8C24×C3
hypercenterC23×C3×C8D3
hypocenterC3C22×C3×M32
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3×C8 ◁ C23×C3×C8

969 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

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, 133371);