Finite Group Databasebeta

C2×#19149378 #26010442

order11008
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC2×#19149378

Splittings

FittingC22×#137×C43 ⋊ C2
SylowC43 ⋊ C2×#3586

Subgroups

subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC4×C43C26
FrattiniC4C25×D43
FittingC22×#137×C43C2
socleC22×C43C23×D4
hypercenterC22×#137D43
hypocenterC43C2×#3586
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

10794 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1006 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1083413);