Finite Group Databasebeta

D43×#2123 #25249331

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

Aliases

direct productD43×#2123

Splittings

FittingC43×#2123 ⋊ C2
SylowC43 ⋊ C2×#2123

Subgroups

subgroupG/H
centerC2C2×#99×D43
commutatorC23×C43C23×C4
FrattiniC2×D4C23×D43
FittingC43×#2123C2
socleC2×C43C22×#99
prime radicalC2×#41×D43C22
cosocleC2×D4×C43C24
hypercenter#2123D43
hypocenterC43C2×#2123
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2123

1214 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, 322302);