Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×#11722576 |
| Sylow | H(5,𝔽2) ⋊ C3×3−1+2 |
1090 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 220 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
273 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72245041, C2×C3×#11722576, #72252958, … |
| maximal normal subgroup of | #72245041, C2×C3×#11722576, #72252958, … |
| maximal quotient of | C2×C3×#11722576 |
Past the SmallGroups library coverage — no SmallGroups id.