Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊#13089712 |
| unambiguous semidirect product | (C7⋊#13089712)⋊C3 |
| derived | C7×C112⋊C3 ⋊ C3×C4 |
| Hall | ΓL(1,𝔽8)×C112⋊C3 ⋊ C4 |
| Hall | C7×C112 ⋊ C3×Dic3 |
| Sylow | C112 ⋊ C3⋊(ΓL(1,𝔽8)⋊C4) |
| Sylow | C7 ⋊ C3×#13089712 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 924 |
Polycyclic presentation:
2,3^2,7,11^2,2|a^2=g,c^a=c^2,d^a=d^6,e^a=e^2f^10,f^a=e^3f^9,d^b=d^2,e^c=e^2f^10,f^c=e^7f^8314 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 219);