Finite Group DatabasebetaFinite Group Databasebeta| order | 17185 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C491⋊C5)⋊C7 |
| unambiguous semidirect product | (C491⋊C7)⋊C5 |
| Fitting, socle, derived, Sylow | C491 ⋊ C5×C7 |
| Hall | C491⋊C7 ⋊ C5 |
| Hall | C491⋊C5 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C491 | C5×C7 |
| LCS | G ▷ C491 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 491 |
Polycyclic presentation:
5,7,491|c^a=c^381,c^b=c^13849 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C491⋊C5)⋊C7, (D491⋊C5)⋊C7 |
| maximal normal subgroup of | C2×(C491⋊C5)⋊C7, (D491⋊C5)⋊C7 |
| maximal quotient of | C2×(C491⋊C5)⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17185, 1);