Finite Group Databasebeta

D43×#1781 #25095717

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productD43×#1781

Splittings

FittingC43×#1781 ⋊ C2
SylowC43 ⋊ C2×#1781

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1781C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D4×D43C2
cosocleC24×C43C24
hypercenter#1781D43
hypocenterC43C2×#1781
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ #1781

6254 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, 168688);