Finite Group Databasebeta

C2×#19135718 #25123826

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19135718

Splittings

FittingC22×#120×C43 ⋊ C2
SylowC43 ⋊ C2×#2021

Subgroups

subgroupG/H
centerC23#13063293
commutator, cosocleC24×C43C24
FrattiniC24C23×D43
FittingC22×#120×C43C2
socleC23×C43#120
hypercenterC22×#120D43
hypocenterC43C2×#2021
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C22×#120

3986 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 196797);