Finite Group Databasebeta

C2×#357×D43 #25249467

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#357×D43

Splittings

FittingC2×C43×#357 ⋊ C2
SylowC43 ⋊ C22×#357

Subgroups

subgroupG/H
centerC23D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC2×C43×#357C2
socleC23×C43C2×D8
prime radicalC22×D8×D43C2
cosocleC2×C8×C43C24
hypercenterC2×#357D43
hypocenterC43C22×#357
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

1470 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, 322438);