Finite Group DatabasebetaFinite Group Databasebeta| order | 30246 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C71 |
| unambiguous semidirect product | C3⋊(C71⋊D71) |
| unambiguous semidirect product | C71⋊D213 |
| Fitting, socle, derived, Hall | C3×C712 ⋊ C2 |
| Sylow | C712 ⋊ D3 |
| Sylow | C3 ⋊ C71⋊D71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C712 | C2 |
| LCS | G ▷ C3×C712 | |
| UCS | C1 | |
296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15123 |
Polycyclic presentation:
2,3,71^2|b^a=b^2,c^a=c^70,d^a=d^707563 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30246, 13);