Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61629 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#62072 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#529 ◁ G | |
1780 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(16,17,21,26)(18,27,30,23)(19,32,34,39)(20,25,22,35)(24,36,40,33)(28,43,45,47)(29,42,31,38)(37,44,41,46);(8,9)(10,13)(11,12)(14,15)(16,18)(17,23)(19,28)(20,29)(21,30)(22,31)(24,37)(25,38)(26,27)(32,47)(33,44)(34,45)(35,42)(36,46)(39,43)(40,41);(16,19,21,34)(17,24,26,40)(18,28,30,45)(20,33,22,36)(23,37,27,41)(25,39,35,32)(29,44,31,46)(38,43,42,47);(9,12)(13,15)(16,20,21,22)(17,25,26,35)(18,29,30,31)(19,33,34,36)(23,38,27,42)(24,39,40,32)(28,44,45,46)(37,43,41,47);(8,10,11,14)(9,13,12,15)(17,26)(18,30)(24,40)(25,35)(28,45)(29,31)(32,39)(44,46)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55060);