Finite Group Databasebeta

C22×(C2×D9)⋊C8 #11857326

order1152
isoclinismisoclinic class of Dic18
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D9)⋊C8

Splittings

FittingC23×C8×C9 ⋊ C2
SylowC9 ⋊ C22×C22⋊C8

Subgroups

subgroupG/H
centerC23×C4C2×D9
commutatorC2×C9C23×C8
FrattiniC2×C3×C4C23×D3
FittingC23×C8×C9C2
socleC24×C3C4×D3
prime radicalC24×D9C4
cosocleC2×C4×C9C24
hypercenterC23×C8D9
hypocenterC9C22×C22⋊C8
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C23×C4 ◁ C23×C8

1608 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 91337);