Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C7⋊C9)⋊Dic121 |
| unambiguous semidirect product | C121⋊(Dic7⋊C9) |
| unambiguous semidirect product | Dic847⋊C9 |
| derived, Hall | C7×C121 ⋊ C4×C9 |
| Hall | C7⋊C9×C121 ⋊ C4 |
| Hall | Dic847 ⋊ C9 |
| Sylow | C121 ⋊ Dic7⋊C9 |
| Hall | C7⋊C9 ⋊ Dic121 |
| Sylow | C7 ⋊ C9×Dic121 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30492 |
Polycyclic presentation:
2,3,7,11,2,3,11|a^2=e,b^3=f,d^11=g^10,c^a=c^6,d^a=d^10g,g^a=g^10,c^b=c^21842 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 4);