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C5×AGL(1,𝔽5)×3−1+2 #72247409

order2700
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×AGL(1,𝔽5)×3−1+2

Splittings

Fitting, HallC52×3−1+2 ⋊ C4
SylowC52 ⋊ C4×3−1+2

Subgroups

subgroupG/H
centerC3×C5C32×AGL(1,𝔽5)
commutatorC3×C5C32×C4×C5
FrattiniC3C32×C5×AGL(1,𝔽5)
FittingC52×3−1+2C4
socleC3×C52C32×C4
prime radicalC32×C5×D5C2×C3
cosocleC3×D5C2×C32×C5
hypercenterC5×3−1+2AGL(1,𝔽5)
hypocenterC5C4×C5×3−1+2
LCSG ▷ C3×C5 ▷ C5
UCSC1 ◁ C3×C5 ◁ C5×3−1+2

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD5×AGL(1,𝔽5)×3−1+2, C5×AGL(1,𝔽5)×AGL(1,ℤ/9), AGL(1,𝔽5)×C5⋊AGL(1,ℤ/9), …
maximal normal subgroup ofD5×AGL(1,𝔽5)×3−1+2, C5×AGL(1,𝔽5)×AGL(1,ℤ/9), AGL(1,𝔽5)×C5⋊AGL(1,ℤ/9)
maximal quotient of3−1+2×AGL(1,ℤ/25)

GAP

Past the SmallGroups library coverage — no SmallGroups id.