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AGL(1,𝔽5)×#1094 #72247477

order2160
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C2

Aliases

direct productAGL(1,𝔽5)×#1094

Splittings

HallC22×AGL(1,𝔽5) ⋊ 3−1+2
SylowC5 ⋊ C4×#1094

Subgroups

subgroupG/H
center, FrattiniC3C3×A4×AGL(1,𝔽5)
commutator, socleC22×C3×C5C32×C4
FittingC22×C32×C5C3×C4
prime radicalC22×C32×D5C2×C3
cosocleC22×C3×D5C2×C32
hypercenterC32A4×AGL(1,𝔽5)
hypocenterC22×C5C4×3−1+2
LCSG ▷ C22×C3×C5 ▷ C22×C5
UCSC1 ◁ C3 ◁ C32

180 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 40 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) = 90

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofA4×AGL(1,𝔽5)×3−1+2, C2×AGL(1,𝔽5)×#1094, AGL(1,𝔽5)×#88907, …
maximal normal subgroup ofA4×AGL(1,𝔽5)×3−1+2, C2×AGL(1,𝔽5)×#1094, AGL(1,𝔽5)×((C22⋊C9)⋊C2)⋊C3
maximal quotient ofC2×AGL(1,𝔽5)×#1094, AGL(1,𝔽5)×#88907

GAP

Past the SmallGroups library coverage — no SmallGroups id.