Finite Group DatabasebetaFinite Group Databasebeta| order | 24108 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C49⋊C3)⋊Dic41 |
| unambiguous semidirect product | Dic2009⋊C3 |
| derived, Hall | C41×C49 ⋊ C3×C4 |
| Hall | Dic2009 ⋊ C3 |
| Hall | C41×C49⋊C3 ⋊ C4 |
| Hall | C49⋊C3 ⋊ Dic41 |
| Sylow | C49 ⋊ C3×Dic41 |
| Sylow | C41 ⋊ (C49⋊C3)⋊C4 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8036 |
Polycyclic presentation:
2,3,7,41,2,7|a^2=e,c^7=f^6,c^a=c^6f,d^a=d^40,f^a=f^6,c^b=c^4f^5,f^b=f^4788 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24108, 4);