Finite Group Databasebeta

C2×#19132779 #25017048

order11008
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#19132779

Splittings

SylowC43 ⋊ C2×#1417

Subgroups

subgroupG/H
centerC2×C4#13063266
commutatorC16×C43C22×C4
FrattiniC2×C16C22×D43
Fitting, prime radicalC2×C43×#508C2
socleC22×C43#357
cosocleC2×C16×C43C23
hypercenterC2×#508D43
hypocenterC43C2×#1417
LCSG ▷ C16×C43 ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C2×#508

294 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1000 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 90019);