Finite Group Databasebeta

C22×C22⋊(C43⋊C16) #25249262

order11008
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C27

Aliases

direct productC22×C22⋊(C43⋊C16)

Splittings

SylowC43 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D43
commutatorC2×C43C23×C16
FrattiniC2×C8C23×D43
FittingC24×C8×C43C2
socleC24×C43C2×C8
prime radicalC25×C43C8
cosocleC2×C8×C43C24
hypercenterC24×C8D43
hypocenterC43C22×C22⋊C16
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C8 ◁ C24×C8

1470 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322233);