Finite Group Databasebeta

D43×#1790 #25095854

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

Aliases

direct productD43×#1790

Splittings

FittingC43×#1790 ⋊ C2
SylowC43 ⋊ C2×#1790

Subgroups

subgroupG/H
centerC22#120×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1790C2
socleC22×C43C2×#120
prime radicalC2×H(5,𝔽2)×D43C2
cosocleC24×C43C24
hypercenter#1790D43
hypocenterC43C2×#1790
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ #1790

4402 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, 168825);