Finite Group Databasebeta

C2×#19143129 #25960156

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

Aliases

direct productC2×#19143129

Splittings

FittingC22×#131×C43 ⋊ C2
SylowC43 ⋊ C2×#2898

Subgroups

subgroupG/H
centerC23C22×D172
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC22×#131×C43C2
socleC23×C43C22×D4
prime radicalC22×#13063372C2
cosocleC2×C4×C43C25
hypercenterC22×#131D43
hypocenterC43C2×#2898
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ C22×#131

4882 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033127);