Finite Group DatabasebetaFinite Group Databasebeta| order | 15225 |
| isoclinism | isoclinic class of C29⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C25 · Schur multiplier (H2) = C1 |
| Fitting, Hall | C3×C25×C29 ⋊ C7 |
| derived, Sylow | C29 ⋊ C3×C7×C25 |
| Hall | C25×C29 ⋊ C3×C7 |
| Hall | C3×C29 ⋊ C7×C25 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2175 |
825 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C25×C29⋊C7, C3×C25×D29⋊C7, C3×D25×C29⋊C7, … |
| maximal normal subgroup of | C2×C3×C25×C29⋊C7, C3×C25×D29⋊C7, C3×D25×C29⋊C7, … |
| maximal quotient of | C2×C3×C25×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15225, 2);