Finite Group Databasebeta

D43×#2161 #25249650

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD43×#2161

Splittings

FittingC43×#2161 ⋊ C2
SylowC43 ⋊ C2×#2161

Subgroups

subgroupG/H
centerC4C2×D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2161C2
socleC2×C43C22×#107
prime radicalC23×D43Q16
cosocleC2×C8×C43C24
hypercenter#2161D43
hypocenterC43C2×#2161
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2161

642 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322621);