Finite Group Databasebeta

D43×#1536 #25064632

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD43×#1536

Splittings

FittingC43×#1536 ⋊ C2
SylowC43 ⋊ C2×#1536

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1536C2
socleC22×C43C22×C22⋊C4
prime radical#532×D43C2
cosocleC42×C43C24
hypercenter#1536D43
hypocenterC43C2×#1536
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1536

1234 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 137603);