Finite Group Databasebeta

C2×#361×D43 #25249546

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#361×D43

Splittings

FittingC2×C43×#361 ⋊ C2
SylowC43 ⋊ C22×#361

Subgroups

subgroupG/H
centerC22#102×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC2×C43×#361C2
socleC22×C43C2×#102
prime radicalC22×D8×D43C2
cosocleC2×C8×C43C24
hypercenterC2×#361D43
hypocenterC43C22×#361
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

1390 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322517);