Finite Group Databasebeta

C2×#19134514 #25095744

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19134514

Splittings

FittingC22×#100×C43 ⋊ C2
SylowC43 ⋊ C2×#1783

Subgroups

subgroupG/H
centerC23C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#100×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D4×D43C2
cosocleC22×C4×C43C24
hypercenterC22×#100D43
hypocenterC43C2×#1783
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#100

5942 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, 168715);