Finite Group Databasebeta

C2×#19132532 #25005721

order11008
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#19132532

Splittings

FittingC2×C43×#349 ⋊ C2
SylowC43 ⋊ C2×#1321

Subgroups

subgroupG/H
centerC2×C4#13063239
commutatorC2×C4×C43C22×C8
FrattiniC2×M16C22×D43
FittingC2×C43×#349C2
socleC22×C43#323
prime radicalC22×#10621898C4
cosocleC2×M16×C43C23
hypercenterC2×#349D43
hypocenterC43C2×#1321
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×M16 ◁ C2×#349

518 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

976 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 78692);