Finite Group Databasebeta

D43×#2197 #25250601

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD43×#2197

Splittings

FittingC43×#2197 ⋊ C2
SylowC43 ⋊ C2×#2197

Subgroups

subgroupG/H
centerC2B(4,𝔽2)×D43
commutator, cosocleC2×D4×C43C24
FrattiniC2×D4C23×D43
FittingC43×#2197C2
socleC2×C43C2×B(4,𝔽2)
prime radicalB(4,𝔽2)×D43C2
hypercenter#2197D43
hypocenterC43C2×#2197
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #2197

1320 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

460 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 323572);