Finite Group Databasebeta

← Prev (#72260078) Next (#72260080) →

D7×#23872 #72260079

order3584
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productD7×#23872

Splittings

FittingC7×#23872 ⋊ C2
SylowC7 ⋊ C2×#23872

Subgroups

subgroupG/H
centerC2D7×#2403
commutator, cosocleC22×C4×C7C25
FrattiniC22×C4C24×D7
FittingC7×#23872C2
socleC2×C7C2×#2403
hypercenter#23872D7
hypocenterC7C2×#23872
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2 ◁ C22×C4 ◁ #23872

12892 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 112

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.