Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#13015 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C2×D8 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
490 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(9,11)(12,13)(14,15)(16,17,20,26,36,45,34,23,22,28,19,25,21,27,37,41)(18,29,31,47,39,44,35,43,33,40,30,42,32,46,38,24);(8,9,10,11)(17,23)(19,34)(20,37)(21,36)(24,40)(25,27)(26,45)(28,41)(29,43)(30,35)(31,38)(32,39)(42,46)(44,47);(13,15)(16,18,22,33)(17,24,28,43)(19,35,20,38)(21,39,36,32)(23,40,41,29)(25,44,26,46)(27,47,45,42)(30,37,31,34)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6003);