Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C72×C19 ⋊ C3×D3 |
| derived | C19×#3862 ⋊ C2×C3 |
| Hall | #22552728 ⋊ C2 |
| Sylow | C72 ⋊ C3⋊(D19⋊C3) |
| Sylow | C19 ⋊ #64418⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C19×#3862 | C2×C3 |
| Fitting, socle | C72×C19 | C3×D3 |
| LCS | G ▷ C19×#3862 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 266 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,4,8,11,10,12)(2,3,5,7,9,14)(6,13)(16,20,21,17,18,22)(19,27,28,23,24,32)(25,33,31,30,29,26);(3,7,8)(4,9,6)(5,12,11)(10,14,13)(15,16,19,24,29,32,31,21,20,25,30,18,22,26,28,33,27,23,17)Polycyclic presentation:
2,3^2,19,7^2|c^a=c^2,d^a=d^18,e^a=e^2f^3,f^a=e^6f^5,d^b=d^11,e^b=e^4,f^b=f^4,e^c=e^4f^4,f^c=f^277 conjugacy classes — view the full character table.
| maximal subgroup of | #45691991, #45692001, #45692003, … |
| maximal normal subgroup of | #45691991, #45692001, #45692003, … |
| maximal quotient of | #45691810, C2×#30660726 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 253);