Finite Group Databasebeta

C22×#14583715 #26010422

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

Aliases

direct productC22×#14583715

Splittings

FittingC22×#137×C43 ⋊ C2
SylowC43 ⋊ C22×#578

Subgroups

subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC4×C43C26
FrattiniC4C25×D43
FittingC22×#137×C43C2
socleC23×C43C22×D4
hypercenterC22×#137D43
hypocenterC43C22×#578
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

10774 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1083393);