Finite Group Databasebeta

C2×#19135138 #25098609

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19135138

Splittings

SylowC43 ⋊ C2×#1913

Subgroups

subgroupG/H
centerC22#14582779
commutatorC23×C43C23×C4
FrattiniC24C23×D43
Fitting, prime radicalC2×C43×#534C2
socleC22×C43#386
cosocleC24×C43C24
hypercenterC2×#534D43
hypocenterC43C2×#1913
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ C2×#534

2078 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

982 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 171580);