Finite Group DatabasebetaFinite Group Databasebeta| order | 17238 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(D169⋊C3) |
| unambiguous semidirect product | (C169⋊C3)⋊D17 |
| unambiguous semidirect product | D2873⋊C3 |
| Fitting, derived, Hall | C17×C169 ⋊ C2×C3 |
| Hall | C17×C169⋊C3 ⋊ C2 |
| Hall | D2873 ⋊ C3 |
| Hall | C169⋊C3 ⋊ D17 |
| Sylow | C169 ⋊ C3×D17 |
| Sylow | C17 ⋊ D169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C17×C169 | C2×C3 |
| Frattini | C13 | C17⋊(D13⋊C3) |
| socle | C13×C17 | D13⋊C3 |
| LCS | G ▷ C17×C169 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2873 |
Polycyclic presentation:
2,3,13,17,13|c^13=e^12,c^a=c^12e,d^a=d^16,e^a=e^12,c^b=c^9e^12,e^b=e^9506 conjugacy classes — view the full character table.
| maximal subgroup of | #26040082⋊C3, #26040083⋊C3, D17×D169⋊C3, … |
| maximal normal subgroup of | #26040082⋊C3, #26040083⋊C3, D17×D169⋊C3, … |
| maximal quotient of | Dic2873⋊C3, C2×C17⋊(D169⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17238, 4);