Finite Group Databasebeta

D43×#2003 #25123485

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productD43×#2003

Splittings

FittingC43×#2003 ⋊ C2
SylowC43 ⋊ C2×#2003

Subgroups

subgroupG/H
centerC22#120×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2003C2
socleC22×C43C2×#120
prime radicalC2×AGL(1,ℤ/8)×D43C2
hypercenter#2003D43
hypocenterC43C2×#2003
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2003

2126 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 196456);