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 | #22552727 ⋊ C2 |
| Sylow | C72 ⋊ D3×C19⋊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:
(1,11,8,13,7,9)(2,3,5,12,4,14)(6,10)(16,17,19)(18,21,22)(20,24,23)(25,29,27)(26,30,28)(31,33,32);(3,7,6)(4,9,10)(5,11,13)(8,14,12)(15,16,18,22,27,32,29,17,20,25,30,19,23,28,21,26,31,33,24)Polycyclic presentation:
2,3^2,19,7^2|c^a=c^2,e^a=f^5,f^a=e^3,d^b=d^7,e^b=e^4,f^b=f^4,e^c=e^2,f^c=f^4140 conjugacy classes — view the full character table.
| maximal subgroup of | #45691992, #45692002, #45692006, … |
| maximal normal subgroup of | #45691992, #45692002, #45692006, … |
| maximal quotient of | #45691811, C2×#30660727 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 254);