Finite Group DatabasebetaFinite Group Databasebeta| order | 2430 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C32 |
| direct product | C5×#4207⋊C3 |
| Fitting, Hall | C5×3−1+4 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C32×C5 |
| Sylow | 3−1+4 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #4207⋊C3 |
| commutator, cosocle, hypocenter | C3×C9 | C2×C32×C5 |
| Frattini | C3 | C32×C5×C3⋊D3 |
| Fitting | C5×3−1+4 | C2 |
| socle | C3×C5 | C32×C3⋊D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C5 | |
362 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 135 |
275 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×#4207⋊C3, C5×#13091120, C5×(#4207⋊C2)⋊C3, … |
| maximal normal subgroup of | D5×#4207⋊C3, C5×(#4207⋊C2)⋊C3, #72247526 |
Past the SmallGroups library coverage — no SmallGroups id.