Finite Group Databasebeta

D43×#3009 #25963005

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productD43×#3009

Splittings

FittingC43×#3009 ⋊ C2
SylowC43 ⋊ C2×#3009

Subgroups

subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3009C2
socleC22×C43C23×D4
prime radicalC2×H(5,𝔽2)×D43C2
hypercenter#3009D43
hypocenterC43C2×#3009
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3009

5062 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, 1035976);