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×#3568 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
6726 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);(3,4,8,10)(5,14,18,16)(6,9,13,19)(7,21,22,12)(11,25,24,15)(17,30,31,28)(20,32,27,23)(26,29,33,34);(4,10)(5,15)(6,13)(11,16)(12,21)(14,24)(17,29)(18,25)(20,27)(26,30)(28,33)(31,34);(3,5,8,18)(4,11,10,24)(6,16,13,14)(7,17,22,31)(9,15,19,25)(12,26,21,33)(20,30,27,28)(23,29,32,34);(3,6,19,4)(5,16,25,11)(7,20,32,12)(8,13,9,10)(14,15,24,18)(17,30,34,26)(21,22,27,23)(28,29,33,31);(3,7,19,32)(4,12,6,20)(5,17,25,34)(8,22,9,23)(10,21,13,27)(11,26,16,30)(14,28,24,33)(15,29,18,31)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55724);