Finite Group Databasebeta

D43×#2048 #25124423

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

Aliases

direct productD43×#2048

Splittings

FittingC43×#2048 ⋊ C2
SylowC43 ⋊ C2×#2048

Subgroups

subgroupG/H
centerC2#394×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2048C2
socleC2×C43C2×#394
prime radicalC2×AGL(1,ℤ/8)×D43C2
hypercenter#2048D43
hypocenterC43C2×#2048
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2048

1450 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 197394);