Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24295 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24296 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2408 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1270 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)(10,21)(11,26)(12,32)(13,36)(14,19)(15,20)(16,24)(17,30)(18,33)(22,38)(23,51)(25,40)(27,42)(28,43)(29,45)(31,44)(34,46)(35,60)(37,41)(39,53)(47,52)(48,66)(49,63)(50,64)(54,56)(55,70)(57,59)(58,67)(61,65)(62,68)(69,71);(8,10,13,24,15,25,14,37)(9,16,19,21,20,41,36,40)(11,27,29,22,31,49,30,50)(12,23,33,52,35,53,34,61)(17,42,44,64,45,63,26,38)(18,39,32,47,46,51,60,65)(28,55,56,48,58,68,57,69)(43,66,59,70,67,71,54,62);(8,11)(9,17)(10,22)(12,28)(13,29)(14,30)(15,31)(16,38)(18,43)(19,44)(20,45)(21,42)(23,48)(24,49)(25,50)(26,36)(27,37)(32,59)(33,56)(34,57)(35,58)(39,62)(40,63)(41,64)(46,67)(47,66)(51,70)(52,68)(53,69)(54,60)(55,61)(65,71);(8,12,14,34,15,35,13,33)(9,18,36,60,20,46,19,32)(10,23,37,61,25,53,24,52)(11,28,30,57,31,58,29,56)(16,39,40,65,41,51,21,47)(17,43,26,54,45,67,44,59)(22,48,27,55,50,69,49,68)(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, 17284);