Finite Group Databasebeta

C2×#19133623 #25068742

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19133623

Splittings

SylowC43 ⋊ C2×#1615

Subgroups

subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#481C2
socleC23×C43#120
prime radicalC2×#121×C43C22
hypercenterC2×#481D43
hypocenterC43C2×#1615
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

1016 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

844 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 141713);