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C4×AGL(1,𝔽5)×3−1+2 #72247360

order2160
automorphism?
homologyAbelianization (H1) = C32×C42 · Schur multiplier (H2) = C4

Aliases

direct productC4×AGL(1,𝔽5)×3−1+2

Splittings

FittingC4×C5×3−1+2 ⋊ C4
HallC5×3−1+2 ⋊ C42
SylowC5 ⋊ C42×3−1+2

Subgroups

subgroupG/H
centerC3×C4C32×AGL(1,𝔽5)
commutatorC3×C5C32×C42
FrattiniC2×C3C2×C32×AGL(1,𝔽5)
FittingC4×C5×3−1+2C4
socleC2×C3×C5C2×C32×C4
prime radicalC2×C32×D5C22×C3
cosocleC2×C3×D5C22×C32
hypercenterC4×3−1+2AGL(1,𝔽5)
hypocenterC5C42×3−1+2
LCSG ▷ C3×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C4×3−1+2

240 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×AGL(1,𝔽5)×AGL(1,ℤ/9), D4×AGL(1,𝔽5)×3−1+2, AGL(1,𝔽5)×C4⋊AGL(1,ℤ/9), …
maximal normal subgroup ofC4×AGL(1,𝔽5)×AGL(1,ℤ/9), D4×AGL(1,𝔽5)×3−1+2, AGL(1,𝔽5)×C4⋊AGL(1,ℤ/9)
maximal quotient ofAGL(1,𝔽5)2×3−1+2, 3−1+2×#87830

GAP

Past the SmallGroups library coverage — no SmallGroups id.