Finite Group Databasebeta

D43×#2180 #25250026

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

Aliases

direct productD43×#2180

Splittings

FittingC43×#2180 ⋊ C2
SylowC43 ⋊ C2×#2180

Subgroups

subgroupG/H
centerC2#442×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2180C2
socleC2×C43C2×#442
prime radical#135×D43C22
cosocleC2×C8×C43C24
hypercenter#2180D43
hypocenterC43C2×#2180
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #2180

646 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, 322997);