Finite Group Databasebeta

D43×#1820 #25096328

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD43×#1820

Splittings

FittingC43×#1820 ⋊ C2
SylowC43 ⋊ C2×#1820

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1820C2
socleC22×C43C22×C22⋊C4
prime radicalC24×D43C23
cosocleC24×C43C24
hypercenter#1820D43
hypocenterC43C2×#1820
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

1566 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, 169299);