Finite Group Databasebeta

D43×#2171 #25249827

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productD43×#2171

Splittings

FittingC43×#2171 ⋊ C2
SylowC43 ⋊ C2×#2171

Subgroups

subgroupG/H
centerC8C2×D4×D43
commutatorC4×C43C23×C8
FrattiniC2×C8C23×D43
FittingC43×#2171C2
socleC2×C43C2×C8×D4
prime radical#135×D43C4
cosocleC2×C8×C43C24
hypercenter#2171D43
hypocenterC43C2×#2171
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C8 ◁ C2×C16 ◁ #2171

654 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322798);