Finite Group Databasebeta

C2×#19136460 #25249887

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19136460

Splittings

SylowC43 ⋊ C2×#2175

Subgroups

subgroupG/H
centerC23D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC22×SD32×C43C2
socleC23×C43C2×D8
prime radicalC22×D8×C43C22
cosocleC2×C8×C43C24
hypercenterC22×SD32D43
hypocenterC43C2×#2175
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

734 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322858);