Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61198 |
| 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×#525 ◁ G | |
2046 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)(8,9,11,13)(10,14,15,12)(16,17)(18,28)(19,32)(20,25)(21,27)(22,26)(23,31)(24,33)(29,43)(30,39)(34,40)(35,38)(36,41)(37,44)(42,46)(45,47);(8,10)(9,12)(11,15)(13,14)(16,18,21,31)(17,23,27,28)(19,29,34,45)(20,35,22,30)(24,37,41,42)(25,39,26,38)(32,47,40,43)(33,46,36,44);(16,19)(17,24)(18,29)(20,33)(21,34)(22,36)(23,37)(25,40)(26,32)(27,41)(28,42)(30,44)(31,45)(35,46)(38,47)(39,43);(10,15)(12,14)(16,20,21,22)(17,25,27,26)(18,30,31,35)(19,33,34,36)(23,38,28,39)(24,40,41,32)(29,44,45,46)(37,47,42,43);(16,20,21,22)(17,26,27,25)(18,30,31,35)(19,33,34,36)(23,39,28,38)(24,32,41,40)(29,44,45,46)(37,43,42,47)385 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54186);