Finite Group Databasebeta

C2×#576×D43 #26010404

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

Aliases

direct productC2×#576×D43

Splittings

FittingC2×C43×#576 ⋊ C2
SylowC43 ⋊ C22×#576

Subgroups

subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC4×C43C26
FrattiniC4C25×D43
FittingC2×C43×#576C2
socleC22×C43C23×D4
hypercenterC2×#576D43
hypocenterC43C22×#576
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#576

11462 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, 1083375);