Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C2×C7×#3563 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| prime radical | C2×C7×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
6458 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 6 generators on 41 points:
(1,2)(35,36,37,38,39,40,41);(3,4)(5,12)(6,9)(7,15)(8,11)(10,16)(13,17)(14,18)(19,20,25,28)(21,23,26,22)(24,32,33,27)(29,30,34,31);(3,5,8,6)(4,9,11,12)(7,13,16,14)(10,17,15,18)(19,21,25,26)(20,22,28,23)(24,29,33,34)(27,30,32,31);(3,6,8,5)(4,9,11,12)(7,14,16,13)(10,17,15,18)(19,22,25,23)(20,26,28,21)(24,30,33,31)(27,34,32,29);(3,4)(5,12)(6,9)(7,10)(8,11)(13,18)(14,17)(15,16)(19,23,25,22)(20,21,28,26)(24,31,33,30)(27,29,32,34);(3,7)(4,10)(5,13)(6,14)(8,16)(9,17)(11,15)(12,18)(19,24)(20,27)(21,29)(22,30)(23,31)(25,33)(26,34)(28,32)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55721);