Finite Group Databasebeta

C2×#19136544 #25250485

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19136544

Splittings

FittingC2×C43×#510 ⋊ C2
SylowC43 ⋊ C2×#2191

Subgroups

subgroupG/H
centerC22#14583031
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#510C2
socleC22×C43#447
prime radicalC2×#14583696C2
hypercenterC2×#510D43
hypocenterC43C2×#2191
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

1128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

712 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 323456);