Finite Group Databasebeta

C2×#19135753 #25123960

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19135753

Splittings

SylowC43 ⋊ C2×#2028

Subgroups

subgroupG/H
centerC23#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#544C2
socleC23×C43#120
prime radicalC24×C43C2×D4
hypercenterC2×#544D43
hypocenterC43C2×#2028
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#544

1238 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

976 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 196931);