Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5×C109 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×Dic5×C109 |
| derived | C5 ⋊ C3×C4×C5×C109 |
| Hall | C3×C52×C109 ⋊ C4 |
| Hall | C52×C109 ⋊ C3×C4 |
| Hall | C3×C52 ⋊ C4×C109 |
| Sylow | C52 ⋊ C3×C4×C109 |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6540 |
13080 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 79);