Finite Group Databasebeta

C2×#19143076 #25960095

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

Aliases

direct productC2×#19143076

Splittings

FittingC2×C43×#413 ⋊ C2
SylowC43 ⋊ C2×#2889

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C43×#413C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#13063372C2
cosocleC2×C4×C43C25
hypercenterC2×#413D43
hypocenterC43C2×#2889
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#413

4770 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, 1033066);