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×#61344 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#535 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#533 ◁ G | |
1748 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)(13,14)(16,17)(18,26)(19,30)(20,24)(21,34)(22,28)(23,32)(25,33)(27,42)(29,37)(31,39)(35,38)(36,46)(40,44)(41,45)(43,47);(8,9,11,12)(10,14,15,13)(16,18,20,28)(17,22,24,26)(19,27,31,43)(21,29,33,45)(23,36,38,40)(25,37,34,41)(30,47,39,42)(32,44,35,46);(16,19,20,31)(17,23,24,38)(18,27,28,43)(21,35,33,32)(22,36,26,40)(25,39,34,30)(29,46,45,44)(37,42,41,47);(8,10,11,15)(9,13,12,14)(18,28)(22,26)(27,43)(29,45)(36,40)(37,41)(42,47)(44,46);(17,24)(18,28)(23,38)(25,34)(27,43)(29,45)(30,39)(44,46)385 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54332);