Finite Group DatabasebetaFinite Group Databasebeta| order | 17459 |
| automorphism | ? |
| homology | Abelianization (H1) = C13×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C79⋊C13 |
| unambiguous semidirect product | C79⋊(C13×C17) |
| unambiguous semidirect product | (C17×C79)⋊C13 |
| Fitting, socle, Hall | C17×C79 ⋊ C13 |
| derived, Sylow | C79 ⋊ C13×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C79⋊C13 |
| commutator, cosocle, hypocenter | C79 | C13×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C79 | C13 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C17 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1343 |
323 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C17×C79⋊C13, C17×D79⋊C13, D17×C79⋊C13, … |
| maximal normal subgroup of | C2×C17×C79⋊C13, C17×D79⋊C13, D17×C79⋊C13, … |
| maximal quotient of | C2×C17×C79⋊C13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17459, 1);