Finite Group Databasebeta

C2×#19139722 #25266728

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19139722

Splittings

FittingC22×#126×C43 ⋊ C2
SylowC43 ⋊ C2×#2559

Subgroups

subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×#126×C43C2
socleC24×C43C24
prime radicalC22×#13063298C2
hypercenterC22×#126D43
hypocenterC43C2×#2559
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#126

3266 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1252 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 339699);