Finite Group Databasebeta

C22×#64110 #11918453

order1152
isoclinismisoclinic class of #634
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C3

Aliases

direct productC22×#64110

Splittings

FittingC23×C32×C8 ⋊ C2
SylowC32 ⋊ C22×#131

Subgroups

subgroupG/H
centerC22×C8C2×C3⋊D3
commutatorC2×C32C24×C4
FrattiniC4C24×C3⋊D3
FittingC23×C32×C8C2
socleC23×C32C22×C4
prime radicalC22×#3828C2
cosocleC32×C4C25
hypercenterC23×C8C3⋊D3
hypocenterC32C22×#131
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C8 ◁ C23×C8

4512 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, 152464);