Finite Group Databasebeta

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AGL(1,𝔽5)×#92259 #72247407

order9720
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3

Aliases

direct productAGL(1,𝔽5)×#92259

Splittings

Fitting, HallC5×#6891 ⋊ C2×C4
Sylow#6891 ⋊ C2×AGL(1,𝔽5)
SylowC5 ⋊ C4×#92259

Subgroups

subgroupG/H
centerC3C3×AGL(1,𝔽5)×(C3⋊D3)⋊C3
commutatorC33×C5C2×C32×C4
FrattiniC32C32×D3×AGL(1,𝔽5)
FittingC5×#6891C2×C4
socleC32×C5C32×C4×D3
prime radicalC32×D5×C3⋊D3C2×C3
cosocleC33×D5C22×C32
hypercenterC32AGL(1,𝔽5)×(C3⋊D3)⋊C3
hypocenterC32×C5C2×C4×3−1+2
LCSG ▷ C33×C5 ▷ C32×C5
UCSC1 ◁ C3 ◁ C32

768 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 90

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×(((C3⋊D3)⋊C9)⋊C2)⋊C3
maximal normal subgroup ofAGL(1,𝔽5)×(((C3⋊D3)⋊C9)⋊C2)⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.