Finite Group Databasebeta

C2×#19135713 #25123794

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19135713

Splittings

SylowC43 ⋊ C2×#2020

Subgroups

subgroupG/H
centerC23#13063297
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC22×#137×C43C2
socleC23×C43#121
prime radicalC22×#41×C43C22
hypercenterC22×#137D43
hypocenterC43C2×#2020
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

1902 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, 196765);