Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13402 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13403 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C2×C7×#41 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ C2×C7×#131 ◁ G | |
384 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)(8,9,14,19)(10,20,25,40)(11,26,31,61)(12,32,34,17)(13,35,37,59)(15,24,41,22)(16,42,46,29)(18,47,49,33)(21,51,54,71)(23,39,58,69)(27,62,52,70)(28,60,30,48)(36,45,63,44)(38,66,68,56)(43,65,67,53)(50,55,64,57);(8,10)(9,15)(11,27)(12,24)(13,23)(14,25)(16,43)(17,40)(18,39)(19,41)(20,32)(21,30)(22,34)(26,51)(28,54)(29,56)(31,52)(33,57)(35,64)(36,65)(37,58)(38,45)(42,66)(44,68)(46,67)(47,55)(48,70)(49,69)(50,59)(53,63)(60,62)(61,71);(8,11,14,31)(9,16,19,46)(10,21)(12,30,34,28)(13,36,37,63)(15,38)(17,45,32,44)(18,48,49,60)(20,43)(22,27)(23,56)(24,52)(25,54)(26,59,61,35)(29,47,42,33)(39,51)(40,67)(41,68)(50,70)(53,57)(55,65)(58,66)(62,64)(69,71)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6391);