Finite Group Databasebeta

C2×#19143075 #25960094

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

Aliases

direct productC2×#19143075

Splittings

FittingC22×#101×C43 ⋊ C2
SylowC43 ⋊ C2×#2889

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC22×#101×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#13063373C2
cosocleC2×C4×C43C25
hypercenterC22×#101D43
hypocenterC43C2×#2889
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#101

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, 1033065);