Finite Group DatabasebetaFinite Group Databasebeta| order | 30300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×#23758755 |
| derived, Sylow | C101 ⋊ C3×C4×C25 |
| Hall | C3×#14579003 ⋊ C4 |
| Hall | #14579003 ⋊ C3×C4 |
| Hall | C3×#87938 ⋊ C25 |
| Hall | #87938 ⋊ C3×C25 |
| Hall | C3×C101 ⋊ C4×C25 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7575 |
375 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30300, 14);