Finite Group Databasebeta

C22×#14582653 #25093947

order11008
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C28

Aliases

direct productC22×#14582653

Splittings

SylowC43 ⋊ C22×#336

Subgroups

subgroupG/H
centerC24×C4C2×D43
commutatorC2×C43C22×C4×C8
FrattiniC22×C4C23×D43
FittingC24×C8×C43C2
socle, prime radicalC25×C43C2×C4
cosocleC22×C4×C43C24
hypercenterC24×C8D43
hypocenterC43C22×#336
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C24×C4 ◁ C24×C8

3086 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, 166918);