Finite Group Databasebeta

C2×#19147748 #26003123

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#19147748

Splittings

FittingC2×C43×#504 ⋊ C2
SylowC43 ⋊ C2×#3417

Subgroups

subgroupG/H
centerC22C22×D344
commutator, cosocleC8×C43C25
FrattiniC8C24×D43
FittingC2×C43×#504C2
socleC22×C43C22×D8
hypercenterC2×#504D43
hypocenterC43C2×#3417
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ C2×#504

2022 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1076094);