Finite Group Databasebeta

C22×#14582656 #25093969

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC22×#14582656

Splittings

SylowC43 ⋊ C22×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC22×C4C4×Dic43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC23×M16×C43C2
socleC23×C43#95
prime radicalC25×C43D4
cosocleC22×C4×C43C24
hypercenterC23×M16D43
hypocenterC43C22×H(3,ℤ/4)
LCSG ▷ C4×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×M16

2270 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 166940);