Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#24810 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2416 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#575 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 71 points:
(1,2,3,4,5,6,7)(8,9,13,36,15,20,14,19)(10,21,24,16,26,40,25,41)(11,27,37,17,31,44,30,45)(12,32,33,18,35,60,34,46)(22,38,28,42,50,64,49,63)(23,51,52,47,54,39,53,65)(29,43,61,59,58,67,57,55)(48,66,56,70,69,71,68,62);(8,10,13,24,15,26,14,25)(9,16,19,21,20,41,36,40)(11,28,30,22,31,49,37,50)(12,23,33,52,35,54,34,53)(17,42,44,64,45,63,27,38)(18,39,32,47,46,51,60,65)(29,56,57,48,58,68,61,69)(43,66,59,70,67,71,55,62);(8,11)(9,17)(10,22)(12,29)(13,30)(14,37)(15,31)(16,38)(18,43)(19,44)(20,45)(21,42)(23,48)(24,49)(25,28)(26,50)(27,36)(32,59)(33,57)(34,61)(35,58)(39,62)(40,63)(41,64)(46,67)(47,66)(51,70)(52,68)(53,56)(54,69)(55,60)(65,71);(8,12,14,34,15,35,13,33)(9,18,36,60,20,46,19,32)(10,23,25,53,26,54,24,52)(11,29,37,61,31,58,30,57)(16,39,40,65,41,51,21,47)(17,43,27,55,45,67,44,59)(22,48,28,56,50,69,49,68)(38,62,63,71,64,70,42,66)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17798);