Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8790 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C2×C8 |
| direct product | C7×#8793 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #382 |
| commutator | C42 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C23×C7 | #124 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(9,10)(11,12)(14,15)(16,17)(18,26,30,22)(19,31,33,46)(20,25)(21,24)(23,32,37,41)(27,34)(28,42)(29,39,40,36)(35,43)(38,47)(44,45);(8,9,11,10,13,15,12,14)(16,18,27,40,21,30,20,29)(17,22,34,39,24,26,25,36)(19,28,41,47,33,44,32,43)(23,35,46,42,37,38,31,45);(8,10,12,9,13,14,11,15)(16,19,21,33)(17,23)(18,28,30,44)(20,32,27,41)(22,35)(24,37)(25,31)(26,38)(29,43,40,47)(34,46)(36,45)(39,42)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1781);