Finite Group Databasebeta

D43×#1856 #25097397

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

Aliases

direct productD43×#1856

Splittings

FittingC43×#1856 ⋊ C2
SylowC43 ⋊ C2×#1856

Subgroups

subgroupG/H
centerC22#120×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1856C2
socleC22×C43C2×#120
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1856D43
hypocenterC43C2×#1856
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1856

1706 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 170368);