Finite Group Databasebeta

C22×#137×D43 #26010392

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

Aliases

direct productC22×#137×D43

Splittings

FittingC22×#137×C43 ⋊ C2
SylowC43 ⋊ C23×#137

Subgroups

subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC4×C43C26
FrattiniC4C25×D43
FittingC22×#137×C43C2
socleC23×C43C22×D4
prime radicalC22×#41×D43C2
hypercenterC22×#137D43
hypocenterC43C23×#137
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

11166 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1083363);