Finite Group Databasebeta

C22×#63376 #11857748

order1152
isoclinismisoclinic class of Dic36
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#63376

Splittings

SylowC9 ⋊ C22×#103

Subgroups

subgroupG/H
centerC24D36
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC23×C8×C9C2
socle, prime radicalC24×C3D12
cosocleC2×C4×C9C24
hypercenterC23×C8D9
hypocenterC9C22×#103
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

1224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1152

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 91759);