Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C43×C49 ⋊ C3×C4 |
| Hall | C43×Dic49 ⋊ C3 |
| Hall | #20263467 ⋊ C4 |
| Hall | Dic49 ⋊ C43⋊C3 |
| Sylow | C49 ⋊ C4×C43⋊C3 |
| Sylow | C43 ⋊ (C49⋊C3)⋊C4 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8428 |
Polycyclic presentation:
2,3,7,43,2,7|a^2=e,c^7=f^6,c^a=c^6f,f^a=f^6,c^b=c^2f^3,d^b=d^36,f^b=f^2756 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 17);