Finite Group Databasebeta

C2×#19135136 #25098607

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

Aliases

direct productC2×#19135136

Splittings

FittingC2×C43×#342 ⋊ C2
SylowC43 ⋊ C2×#1913

Subgroups

subgroupG/H
centerC22#14582777
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC2×C43×#342C2
socleC22×C43#386
prime radicalC2×#14583461C2
cosocleC24×C43C24
hypercenterC2×#342D43
hypocenterC43C2×#1913
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

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, 171578);