Finite Group DatabasebetaFinite Group Databasebeta| order | 3120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×AGL(1,𝔽5)×D13⋊C3 |
| Fitting, socle | C2×C5×C13 ⋊ C2×C3×C4 |
| derived, Hall | C5×C13 ⋊ C22×C3×C4 |
| Hall | C2×AGL(1,𝔽5)×D13 ⋊ C3 |
| Hall | C5×C13⋊C3 ⋊ C22×C4 |
| Hall | C13⋊C3 ⋊ C22×AGL(1,𝔽5) |
| Sylow | C13 ⋊ C22×C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×C4×D13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽5)×D13⋊C3 |
| commutator, hypocenter | C5×C13 | C22×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C13 | C2×C3×C4 |
| prime radical | C2×D5×D13⋊C3 | C2 |
| cosocle | D5×C13 | C23×C3 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C2 | |
216 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 130 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×AGL(1,𝔽13), D13⋊C3×D5⋊AGL(1,𝔽5), D3×AGL(1,𝔽5)×D13⋊C3 |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×AGL(1,𝔽13) |
| maximal quotient of | D13⋊C3×D5⋊AGL(1,𝔽5), D3×AGL(1,𝔽5)×D13⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.