Finite Group Databasebeta

D43×#1848 #25097050

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

Aliases

direct productD43×#1848

Splittings

FittingC43×#1848 ⋊ C2
SylowC43 ⋊ C2×#1848

Subgroups

subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1848C2
socleC22×C43C22×C4⋊C4
prime radicalC23×D43C2×Q8
cosocleC22×C4×C43C24
hypercenter#1848D43
hypocenterC43C2×#1848
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1848

1046 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, 170021);