Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24423 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3586 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1284 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)(8,9,15,37,14,19,13,20)(10,21,35,40,25,16,24,46)(11,26,36,17,29,47,30,43)(12,31,33,44,34,18,32,45)(22,50,56,48,52,41,27,38)(23,39,54,65,55,49,53,64)(28,57,61,62,59,67,60,42)(51,69,58,63,70,66,71,68);(8,10,14,25)(9,16,19,21)(11,27,29,56)(12,23,34,55)(13,35,15,24)(17,41,43,50)(18,39,31,49)(20,46,37,40)(22,36,52,30)(26,38,47,48)(28,58,59,71)(32,54,33,53)(42,66,62,69)(44,65,45,64)(51,60,70,61)(57,63,67,68);(8,11)(9,17)(10,22)(12,28)(13,36)(14,29)(15,30)(16,38)(18,42)(19,43)(20,47)(21,48)(23,51)(24,56)(25,52)(26,37)(27,35)(31,62)(32,61)(33,60)(34,59)(39,63)(40,50)(41,46)(44,57)(45,67)(49,68)(53,58)(54,71)(55,70)(64,66)(65,69);(8,12)(9,18)(10,23)(11,28)(13,33)(14,34)(15,32)(16,39)(17,42)(19,31)(20,45)(21,49)(22,51)(24,54)(25,55)(26,57)(27,58)(29,59)(30,61)(35,53)(36,60)(37,44)(38,63)(40,65)(41,66)(43,62)(46,64)(47,67)(48,68)(50,69)(52,70)(56,71)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17411);