Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊((C11⋊C25)⋊D11) |
| unambiguous semidirect product | (C2×C3)⋊((C11⋊C25)⋊D11) |
| unambiguous semidirect product | (C2×C11⋊C25)⋊D33 |
| derived, Hall | C3×C112 ⋊ C22×C25 |
| Hall | C3×C11×C11⋊C25 ⋊ C22 |
| Hall | C11×C11⋊C25 ⋊ C2×D3 |
| Hall | C2×C3⋊(C11⋊D11) ⋊ C25 |
| Sylow | C112 ⋊ C2×D3×C25 |
| Sylow | C3 ⋊ C2×(C11⋊C25)⋊D11 |
160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1650 |
1230 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 282);