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C22×3−1+2⋊AGL(1,𝔽5) #72247333

order2160
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC22×3−1+2⋊AGL(1,𝔽5)

Splittings

FittingC22×C5×3−1+2 ⋊ C4
derivedC5×C9 ⋊ C22×C3×C4
HallC5×3−1+2 ⋊ C22×C4
Sylow3−1+2 ⋊ C22×AGL(1,𝔽5)
SylowC5 ⋊ C22×3−1+2⋊C4

Subgroups

subgroupG/H
center, hypercenterC223−1+2⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C22×C3×C4
FrattiniC3C22×C3×ΓL(1,𝔽16)
FittingC22×C5×3−1+2C4
socleC22×C3×C5C3×Dic3
prime radicalC22×C32×D5D3
cosocleC9×D5C23×C3
LCSG ▷ C5×C9
UCSC1 ◁ C22

356 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 127 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

124 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×AGL(1,𝔽5)×AGL(1,ℤ/9), C22×#72222340, D4×3−1+2⋊AGL(1,𝔽5), …
maximal normal subgroup ofC22×AGL(1,𝔽5)×AGL(1,ℤ/9), D4×3−1+2⋊AGL(1,𝔽5), #72247459, …
maximal quotient ofC22×#72222340, D4×3−1+2⋊AGL(1,𝔽5), C2×#72222361

GAP

Past the SmallGroups library coverage — no SmallGroups id.