Finite Group Databasebeta

C2×#19136052 #25125531

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19136052

Splittings

SylowC43 ⋊ C2×#2081

Subgroups

subgroupG/H
centerC22#14582824
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#418C2
socleC22×C43#397
prime radicalC23×D4×C43C22
hypercenterC2×#418D43
hypocenterC43C2×#2081
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#418

1006 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

970 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 198502);