Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C8 · Schur multiplier (H2) = C24 |
| direct product | C7×#12987 |
| subgroup | G/H | |
|---|---|---|
| center | C7×C8 | #121 |
| commutator | C2×C4 | C22×C7×C8 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| socle | C2×C7 | #1869 |
| prime radical | C7×#575 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C7×C8 ◁ C22×C7×C8 ◁ G | |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 71 points:
(1,2,3,4,5,6,7)(8,9,13,20,14,21,35,50,15,18,36,37,12,19,32,47)(10,16,25,40,24,39,56,66,23,41,33,48,30,45,61,68)(11,26,29,59,28,44,60,49,27,46,34,62,31,17,42,43)(22,51,53,69,54,38,63,65,55,58,57,71,52,64,70,67);(8,10,13,33,14,24,35,61,15,23,36,25,12,30,32,56)(9,16,37,40,21,39,47,66,18,41,20,48,19,45,50,68)(11,22,34,53,28,54,42,63,27,55,29,57,31,52,60,70)(17,38,43,67,26,58,59,69,44,64,49,65,46,51,62,71);(8,11)(9,17)(10,22)(12,31)(13,34)(14,28)(15,27)(16,38)(18,44)(19,46)(20,49)(21,26)(23,55)(24,54)(25,57)(29,36)(30,52)(32,60)(33,53)(35,42)(37,43)(39,58)(40,67)(41,64)(45,51)(47,59)(48,65)(50,62)(56,70)(61,63)(66,69)(68,71)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 5975);