Finite Group DatabasebetaFinite Group Databasebeta| order | 17170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(D101⋊C5) |
| unambiguous semidirect product | (C101⋊C5)⋊D17 |
| unambiguous semidirect product | D1717⋊C5 |
| Fitting, socle, derived, Hall | C17×C101 ⋊ C2×C5 |
| Hall | C17×C101⋊C5 ⋊ C2 |
| Hall | D1717 ⋊ C5 |
| Hall | C101⋊C5 ⋊ D17 |
| Sylow | C101 ⋊ C5×D17 |
| Sylow | C17 ⋊ D101⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C101 | C2×C5 |
| LCS | G ▷ C17×C101 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1717 |
Polycyclic presentation:
2,5,17,101|c^a=c^16,d^a=d^100,d^b=d^95220 conjugacy classes — view the full character table.
| maximal subgroup of | #20293554⋊C5, #20293555⋊C5, D17×D101⋊C5, … |
| maximal normal subgroup of | #20293554⋊C5, #20293555⋊C5, D17×D101⋊C5, … |
| maximal quotient of | Dic1717⋊C5, C2×C17⋊(D101⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17170, 12);