Finite Group DatabasebetaFinite Group Databasebeta| order | 19074 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C11⋊((C17⋊D17)⋊C3) |
| unambiguous semidirect product | (C11⋊(C17⋊D17))⋊C3 |
| Fitting, socle, derived, Hall | C11×C172 ⋊ C2×C3 |
| Hall | C11×C172⋊C3 ⋊ C2 |
| Hall | C11⋊(C17⋊D17) ⋊ C3 |
| Hall | C172⋊C3 ⋊ D11 |
| Sylow | C172 ⋊ C3×D11 |
| Sylow | C11 ⋊ (C17⋊D17)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C172 | C2×C3 |
| LCS | G ▷ C11×C172 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 62 |
| transitive degree | μt(G) = 561 |
A minimal faithful permutation representation — 2 generators on 62 points:
(1,2,4)(3,17,18,7,8,30)(5,27,29,12,13,22)(6,11,35,15,16,26)(9,19,10,20,21,23)(14,43,46,31,32,51)(24,49,34,42,40,28)(25,45,37,38,44,33)(36,50,39,41,48,47)(53,54)(55,56)(57,58)(59,60)(61,62);(1,3,9,22,40,50,51,26,45,44,35,46,48,49,29,20,7)(2,5,14,33,47,21,17,28,6,15,34,8,19,39,37,31,12)(4,10,24,43,38,16,36,13,30,18,27,41,11,25,32,42,23)(52,53,55,57,59,61,62,60,58,56,54)Polycyclic presentation:
2,3,11,17^2|c^a=c^10,d^a=d^16,e^a=e^16,d^b=d^2e^16,e^b=d^7e^14549 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19074, 13);