Finite Group Databasebeta

C22×#14582705 #25249519

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#14582705

Splittings

FittingC22×#108×C43 ⋊ C2
SylowC43 ⋊ C22×#359

Subgroups

subgroupG/H
centerC22×C4#10621882
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC22×#108×C43C2
socleC23×C43#102
prime radicalC22×#13063347C2
cosocleC2×C8×C43C24
hypercenterC22×#108D43
hypocenterC43C22×#359
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8 ◁ C22×#108

1174 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322490);