Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61338 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C2×C7×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#533 ◁ G | |
1732 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)(13,14)(16,17,21,25)(18,27,29,23)(19,31,33,41)(20,26,22,35)(24,36,40,32)(28,43,44,47)(30,39,34,38)(37,46,42,45);(8,9,11,12)(10,14,15,13)(16,18,21,29)(17,23,25,27)(19,28,33,44)(20,34,22,30)(24,37,40,42)(26,39,35,38)(31,47,41,43)(32,46,36,45);(16,19)(17,24)(18,28)(20,32)(21,33)(22,36)(23,37)(25,40)(26,41)(27,42)(29,44)(30,45)(31,35)(34,46)(38,47)(39,43);(8,10,11,15)(9,13,12,14)(17,25)(18,29)(24,40)(26,35)(28,44)(30,34)(31,41)(45,46);(16,20,21,22)(17,26,25,35)(18,30,29,34)(19,32,33,36)(23,38,27,39)(24,41,40,31)(28,45,44,46)(37,47,42,43)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54326);