Finite Group DatabasebetaFinite Group Databasebeta| order | 4860 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D5×#4184⋊C3 |
| Fitting, Hall | C5×#6910 ⋊ C22 |
| derived | C5×#731 ⋊ C22×C3 |
| Sylow | #6910 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×#4184⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×#731 | C22×C3 |
| Frattini | C32 | C3×D5×C3⋊D3 |
| Fitting | C5×#6910 | C22 |
| socle | C3×C5 | C2×C3×#272 |
| LCS | G ▷ C5×#731 | |
| UCS | C1 | |
456 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 135 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#4184⋊C3, D5×#13091120, D5×(#4176⋊C2)⋊C3, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#4184⋊C3, D5×(#4176⋊C2)⋊C3, #72268699 |
Past the SmallGroups library coverage — no SmallGroups id.