Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×#84128⋊C3 |
| Fitting | C27×C3 ⋊ C2×C3 |
11452 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 11452 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×AΣL(1,𝔽64), C2×#72228419, C2×#72229182 |
| maximal normal subgroup of | C2×D3×AΣL(1,𝔽64), C2×#72228419, C2×#72229182 |
Past the SmallGroups library coverage — no SmallGroups id.