Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊#20258408 |
| unambiguous semidirect product | (C2×C3)⋊#20258408 |
| derived, Hall | C3×C112 ⋊ C22×C25 |
| Hall | C3×#15690028 ⋊ C22 |
| Hall | #15690028 ⋊ C2×D3 |
| Hall | C2×C11×D33 ⋊ C25 |
| Sylow | C112 ⋊ C2×D3×C25 |
| Sylow | C3 ⋊ C2×#20258408 |
128 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3300 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 281);