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D5×AGL(1,𝔽5)×AGL(1,ℤ/9) #72247456

order10800
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productD5×AGL(1,𝔽5)×AGL(1,ℤ/9)

Splittings

Fitting, HallC52×3−1+2 ⋊ C22×C4
derivedC52×C9 ⋊ C22×C3×C4
Sylow3−1+2 ⋊ C2×D5×AGL(1,𝔽5)
SylowC52 ⋊ C2×C4×AGL(1,ℤ/9)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, hypocenterC52×C9C22×C3×C4
FrattiniC3C3×D3×D5×AGL(1,𝔽5)
FittingC52×3−1+2C22×C4
socleC3×C52C2×C3×C4×D3
prime radicalD52×AGL(1,ℤ/9)C2
cosocleC5×C9×D5C23×C3
LCSG ▷ C52×C9
UCSC1

712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)2×AGL(1,ℤ/9)
maximal normal subgroup ofAGL(1,𝔽5)2×AGL(1,ℤ/9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.