Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24411 |
| 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 | |
1294 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)(10,20,24,15)(11,25)(12,30,32,17)(13,18)(14,19)(16,28)(21,46,49,36)(22,37)(23,44,34,38)(26,53,52,39)(27,54,56,40)(29,45)(31,58,61,42)(33,43)(35,41)(47,50)(48,68)(51,63)(55,71)(57,67,60,65)(59,66)(62,69)(64,70);(8,10,13,24)(9,15,18,20)(11,26,28,52)(12,22,32,50)(14,34,33,23)(16,39,25,53)(17,37,30,47)(19,44,43,38)(21,35,49,29)(27,55,56,70)(31,59,61,51)(36,45,46,41)(40,64,54,71)(42,66,58,63)(48,60,69,57)(62,67,68,65);(8,11)(9,16)(10,21)(12,27)(13,28)(14,35)(15,36)(17,40)(18,25)(19,45)(20,46)(22,48)(23,52)(24,49)(26,34)(29,33)(30,54)(31,60)(32,56)(37,62)(38,53)(39,44)(41,43)(42,67)(47,68)(50,69)(51,70)(55,59)(57,61)(58,65)(63,71)(64,66);(8,12)(9,17)(10,22)(11,27)(13,32)(14,31)(15,37)(16,40)(18,30)(19,42)(20,47)(21,48)(23,51)(24,50)(25,54)(26,55)(28,56)(29,57)(33,61)(34,59)(35,60)(36,62)(38,63)(39,64)(41,65)(43,58)(44,66)(45,67)(46,68)(49,69)(52,70)(53,71)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17399);