Finite Group Databasebeta

C22×#14582683 #25249294

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#14582683

Splittings

SylowC43 ⋊ C22×#350

Subgroups

subgroupG/H
centerC22×C8C22⋊D43
commutatorC4×C43C23×C8
FrattiniC2×C8C23×D43
FittingC22×#131×C43C2
socleC23×C43C22⋊C8
prime radicalC22×#41×C43C4
cosocleC2×C8×C43C24
hypercenterC22×#131D43
hypocenterC43C22×#350
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C22×#131

1174 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322265);