Finite Group DatabasebetaFinite Group Databasebeta| order | 17185 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C491⋊C5 |
| unambiguous semidirect product | (C7×C491)⋊C5 |
| Fitting, socle, Hall | C7×C491 ⋊ C5 |
| derived, Sylow | C491 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C491⋊C5 |
| commutator, cosocle, hypocenter | C491 | C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C491 | C5 |
| LCS | G ▷ C491 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3437 |
721 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C7×C491⋊C5, C7×D491⋊C5, D7×C491⋊C5, … |
| maximal normal subgroup of | C2×C7×C491⋊C5, C7×D491⋊C5, D7×C491⋊C5, … |
| maximal quotient of | C2×C7×C491⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17185, 3);