Finite Group Databasebeta

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D7×#32898 #72259491

order3584
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C213

Aliases

direct productD7×#32898

Splittings

FittingC7×#32898 ⋊ C2
SylowC7 ⋊ C2×#32898

Subgroups

subgroupG/H
centerC22C2×D7×#120
commutator, cosocleC24×C7C25
FrattiniC24C24×D7
FittingC7×#32898C2
socleC22×C7C22×#120
hypercenter#32898D7
hypocenterC7C2×#32898
LCSG ▷ C24×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C25 ◁ #32898

39956 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 224

Conjugacy classes & character table

245 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.