Finite Group Databasebeta

D43×#2135 #25249437

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD43×#2135

Splittings

FittingC43×#2135 ⋊ C2
SylowC43 ⋊ C2×#2135

Subgroups

subgroupG/H
centerC2C2×#99×D43
commutatorC2×C4×C43C23×C4
FrattiniC2×Q8C23×D43
FittingC43×#2135C2
socleC2×C43C22×#99
prime radicalC2×#41×D43C22
cosocleC2×Q8×C43C24
hypercenter#2135D43
hypocenterC43C2×#2135
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2135

1198 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, 322408);