Finite Group Databasebeta

C22×#14583706 #26010412

order11008
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×#14583706

Splittings

FittingC22×#135×C43 ⋊ C2
SylowC43 ⋊ C22×#577

Subgroups

subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC4×C43C26
FrattiniC4C25×D43
FittingC22×#135×C43C2
socleC23×C43C22×D4
hypercenterC22×#135D43
hypocenterC43C22×#577
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#135

11118 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, 1083383);