Finite Group Databasebeta

C2×#19140194 #25267257

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

Aliases

direct productC2×#19140194

Splittings

FittingC22×#126×C43 ⋊ C2
SylowC43 ⋊ C2×#2601

Subgroups

subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×#126×C43C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC22×#126D43
hypocenterC43C2×#2601
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#126

2898 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, 340228);