Finite Group Databasebeta

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AGL(1,𝔽5)×3−1+2⋊C4 #72247361

order2160
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C4

Aliases

direct productAGL(1,𝔽5)×3−1+2⋊C4

Splittings

derivedC5×C9 ⋊ C3×C42
HallC5×3−1+2 ⋊ C42
Sylow3−1+2 ⋊ C4×AGL(1,𝔽5)
SylowC5 ⋊ C4×3−1+2⋊C4

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽5)×AGL(1,ℤ/9)
commutator, hypocenterC5×C9C3×C42
FrattiniC2×C3C3×D3×AGL(1,𝔽5)
FittingC2×C5×3−1+2C2×C4
socleC2×C3×C5C3×C4×D3
prime radicalC2×C32×D5C2×D3
cosocleC2×C9×D5C22×C3
LCSG ▷ C5×C9
UCSC1 ◁ C2

196 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 66 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

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×AGL(1,𝔽5)×AGL(1,ℤ/9), AGL(1,𝔽5)×#611⋊C3, #72247437, …
maximal normal subgroup ofC4×AGL(1,𝔽5)×AGL(1,ℤ/9), AGL(1,𝔽5)×#611⋊C3, #72247459
maximal quotient of#72247437, AGL(1,𝔽5)×3−1+2⋊AGL(1,𝔽5), #72254572, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.