Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | C3×#27130863 |
| derived, Hall | C5×#10597245 ⋊ C3×C4 |
| Hall | C3×C5×#10597245 ⋊ C4 |
| Hall | C3×C112 ⋊ #1039 |
| Sylow | C112 ⋊ C3×#1039 |
152 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 660 |
534 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 386);