Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#11717473 |
| Fitting | C2×C3×C4×C52 ⋊ C22 |
| Hall | C3×C52 ⋊ H(5,𝔽2) |
| Sylow | C52 ⋊ C3×H(5,𝔽2) |
772 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
267 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#13107821 |
| maximal normal subgroup of | C3×#13107821 |
Past the SmallGroups library coverage — no SmallGroups id.