Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×C3×AΣL(1,𝔽64) |
| Fitting | C2×C3×#2846 ⋊ C3 |
| Sylow | C2×#2846 ⋊ C32 |
11566 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 11566 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#11713200, C2×D3×AΣL(1,𝔽64), C2×#72228412, … |
| maximal normal subgroup of | C2×C3×#11713200, C2×D3×AΣL(1,𝔽64), C2×#72228412 |
| maximal quotient of | C2×C3×#72215851 |
Past the SmallGroups library coverage — no SmallGroups id.