Finite Group Databasebeta

C2×#19146255 #25971759

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

Aliases

direct productC2×#19146255

Splittings

FittingC22×#137×C43 ⋊ C2
SylowC43 ⋊ C2×#3278

Subgroups

subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#137×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583568C2
hypercenterC22×#137D43
hypocenterC43C2×#3278
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

2794 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

982 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1044730);