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×#3564 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| prime radical | C2×C7×#538 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
6598 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 6 generators on 41 points:
(1,2)(35,36,37,38,39,40,41);(3,4,8,12)(5,13,14,10)(6,17,20,11)(7,9,19,23)(15,25,27,26)(16,24,28,21)(18,31,32,22)(29,34,30,33);(4,9)(5,14)(6,18)(10,24)(12,23)(13,21)(15,29)(16,28)(20,32)(25,26)(27,30)(33,34);(3,5,7,16)(4,10,9,21)(6,15,18,30)(8,14,19,28)(11,25,22,33)(12,13,23,24)(17,26,31,34)(20,27,32,29);(3,6,19,32)(4,11,23,31)(5,15,28,29)(7,18,8,20)(9,22,12,17)(10,25,24,34)(13,26,21,33)(14,27,16,30);(4,9)(10,21)(11,22)(12,23)(13,24)(17,31)(25,33)(26,34)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55722);