Finite Group Databasebeta

C2×#19143054 #25960065

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#19143054

Splittings

FittingC2×C43×#410 ⋊ C2
SylowC43 ⋊ C2×#2883

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#410C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#13063371C2
cosocleC23×C43C25
hypercenterC2×#410D43
hypocenterC43C2×#2883
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#410

5338 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, 1033036);