Finite Group Databasebeta

C2×#19136609 #25250641

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19136609

Splittings

FittingC2×C43×#352 ⋊ C2
SylowC43 ⋊ C2×#2201

Subgroups

subgroupG/H
centerC22#14583087
commutator, cosocleC2×D4×C43C24
FrattiniC2×D4C23×D43
FittingC2×C43×#352C2
socleC22×C43B(4,𝔽2)
prime radicalC2×#13063370C22
hypercenterC2×#352D43
hypocenterC43C2×#2201
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

1136 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

580 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 323612);