Finite Group Databasebeta

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AGL(1,𝔽5)×#611⋊C3 #72247406

order4320
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productAGL(1,𝔽5)×#611⋊C3

Splittings

FittingC22×C5×3−1+2 ⋊ C2×C4
HallC5×3−1+2 ⋊ C4×D4
Sylow3−1+2 ⋊ D4×AGL(1,𝔽5)
SylowC5 ⋊ C4×#611⋊C3

Subgroups

subgroupG/H
centerC2C2×AGL(1,𝔽5)×AGL(1,ℤ/9)
commutatorC2×C5×C9C22×C3×C4
FrattiniC2×C3C2×C3×D3×AGL(1,𝔽5)
FittingC22×C5×3−1+2C2×C4
socleC2×C3×C5C2×C3×C4×D3
prime radicalD5×#611⋊C3C2
cosocleC2×C9×D5C23×C3
hypercenterC22AGL(1,𝔽5)×AGL(1,ℤ/9)
hypocenterC5×C9C3×C4×D4
LCSG ▷ C2×C5×C9 ▷ C5×C9
UCSC1 ◁ C2 ◁ C22

618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

155 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×AGL(1,𝔽5)×AGL(1,ℤ/9), #72254715, #72254735, …
maximal normal subgroup ofD4×AGL(1,𝔽5)×AGL(1,ℤ/9)
maximal quotient of#72254715, #72254735

GAP

Past the SmallGroups library coverage — no SmallGroups id.