Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32870 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#32872 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2826 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
482 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)(8,9,14,19,15,21,13,20)(10,22,26,40,27,50,25,16)(11,28,32,17,33,43,31,44)(12,18,35,48,36,49,37,47)(23,38,29,41,55,64,54,51)(24,52,57,45,59,66,58,39)(30,46,34,42,60,68,61,69)(53,63,56,67,62,70,71,65);(8,10,13,25,15,27,14,26)(9,16,19,22,21,40,20,50)(11,29,31,23,33,54,32,55)(12,24,35,57,36,59,37,58)(17,41,43,64,44,51,28,38)(18,45,47,52,49,39,48,66)(30,56,34,62,60,71,61,53)(42,65,46,70,69,67,68,63);(8,11,15,33)(9,17,21,44)(10,23,27,55)(12,34,36,61)(13,32,14,31)(16,38,40,64)(18,46,49,68)(19,28,20,43)(22,51,50,41)(24,56,59,71)(25,29,26,54)(30,37,60,35)(39,65,45,67)(42,48,69,47)(52,70,66,63)(53,58,62,57);(8,12)(9,18)(10,24)(11,30)(13,37)(14,35)(15,36)(16,39)(17,42)(19,48)(20,47)(21,49)(22,52)(23,53)(25,58)(26,57)(27,59)(28,46)(29,56)(31,61)(32,34)(33,60)(38,63)(40,45)(41,67)(43,68)(44,69)(50,66)(51,65)(54,71)(55,62)(64,70)196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 25860);