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3−1+2×C22⋊AGL(1,𝔽5) #72247378

order2160
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C22

Aliases

direct product3−1+2×C22⋊AGL(1,𝔽5)

Splittings

FittingC22×C5×3−1+2 ⋊ C4
HallC5×3−1+2 ⋊ C22⋊C4
SylowC5 ⋊ C22⋊C4×3−1+2

Subgroups

subgroupG/H
center, FrattiniC2×C3C2×C32×AGL(1,𝔽5)
commutator, socleC2×C3×C5C2×C32×C4
FittingC22×C5×3−1+2C4
prime radicalC22×C32×D5C2×C3
cosocleC2×C3×D5C22×C32
hypercenterC22×3−1+2AGL(1,𝔽5)
hypocenterC5C22⋊C4×3−1+2
LCSG ▷ C2×C3×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×3−1+2

272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×AGL(1,𝔽5)×3−1+2, AGL(1,ℤ/9)×C22⋊AGL(1,𝔽5), #72247459, …
maximal normal subgroup ofD4×AGL(1,𝔽5)×3−1+2, AGL(1,ℤ/9)×C22⋊AGL(1,𝔽5), #72247459
maximal quotient of3−1+2×#87831, 3−1+2×C22⋊#1044

GAP

Past the SmallGroups library coverage — no SmallGroups id.