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C2×D9×D5⋊AGL(1,𝔽5) #72247471

order7200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D9×D5⋊AGL(1,𝔽5)

Splittings

FittingC2×C52×C9 ⋊ C22×C4
derived, HallC52×C9 ⋊ C23×C4
SylowC52 ⋊ C22×C4×D9
SylowC9 ⋊ C22×D5⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC2D9×D5⋊AGL(1,𝔽5)
commutator, hypocenterC52×C9C23×C4
FrattiniC3C2×D3×D5⋊AGL(1,𝔽5)
FittingC2×C52×C9C22×C4
socleC2×C3×C52C2×C4×D3
prime radicalC2×D52×D9C2
cosocleC9×C5⋊D5C24
LCSG ▷ C52×C9
UCSC1 ◁ C2

1578 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD9×#11717375, C2×AGL(1,ℤ/9)×D5⋊AGL(1,𝔽5)
maximal normal subgroup ofD9×#11717375, C2×AGL(1,ℤ/9)×D5⋊AGL(1,𝔽5)
maximal quotient ofD9×#11717375

GAP

Past the SmallGroups library coverage — no SmallGroups id.