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C2×D52×AGL(1,ℤ/9) #72247758

order10800
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC2×D52×AGL(1,ℤ/9)

Splittings

FittingC2×C52×3−1+2 ⋊ C23
derivedC52×C9 ⋊ C24×C3
HallC52×3−1+2 ⋊ C24
Sylow3−1+2 ⋊ C22×D52
SylowC52 ⋊ C23×AGL(1,ℤ/9)

Subgroups

subgroupG/H
center, hypercenterC2D52×AGL(1,ℤ/9)
commutator, cosocle, hypocenterC52×C9C24×C3
FrattiniC3C2×C3×D3×D52
FittingC2×C52×3−1+2C23
socleC2×C3×C52C22×C3×D3
LCSG ▷ C52×C9
UCSC1 ◁ C2

1874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×AGL(1,ℤ/9)×D5⋊AGL(1,𝔽5), AGL(1,ℤ/9)×#87886, AGL(1,ℤ/9)×#87831
maximal normal subgroup ofC2×AGL(1,ℤ/9)×D5⋊AGL(1,𝔽5), AGL(1,ℤ/9)×#87886, AGL(1,ℤ/9)×#87831
maximal quotient ofAGL(1,ℤ/9)×#87886

GAP

Past the SmallGroups library coverage — no SmallGroups id.