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×#62060 |
| 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 | |
1810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(16,17,22,26)(18,23,29,38)(19,30,32,40)(20,25,21,34)(24,35,41,31)(27,42,44,47)(28,37,33,39)(36,43,46,45);(8,9)(10,13)(11,12)(14,15)(16,18)(17,23)(19,27)(20,33)(21,28)(22,29)(24,36)(25,39)(26,38)(30,42)(31,45)(32,44)(34,37)(35,43)(40,47)(41,46);(16,19)(17,24)(18,27)(20,31)(21,35)(22,32)(23,36)(25,40)(26,41)(28,43)(29,44)(30,34)(33,45)(37,42)(38,46)(39,47);(9,12)(13,15)(16,20,22,21)(17,25,26,34)(18,28,29,33)(19,31,32,35)(23,37,38,39)(24,40,41,30)(27,43,44,45)(36,42,46,47);(8,10,11,14)(9,13,12,15)(18,29)(23,38)(27,44)(28,33)(36,46)(37,39)(42,47)(43,45)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55048);