Finite Group Databasebeta

D43×#1568 #25065600

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD43×#1568

Splittings

FittingC43×#1568 ⋊ C2
SylowC43 ⋊ C2×#1568

Subgroups

subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1568C2
socleC22×C43C22×C4⋊C4
prime radicalC23×D43C4⋊C4
cosocleC42×C43C24
hypercenter#1568D43
hypocenterC43C2×#1568
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1568

766 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 138571);