Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#33705 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C7 |
| prime radical | C23×C7 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
578 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17,23,29)(18,25,30,42)(19,24,33,39)(20,27,36,45)(21,26,37,44)(22,38,35,28)(31,43,46,41)(32,47,34,40);(9,12)(13,15)(16,18,21,31,22,32,36,33,23,30,37,46,35,34,20,19)(17,24,27,40,28,41,44,42,29,39,45,47,38,43,26,25);(8,10,11,14)(9,13,12,15)(16,19,20,34,35,46,37,30,23,33,36,32,22,31,21,18)(17,25,26,43,38,47,45,39,29,42,44,41,28,40,27,24);(18,30)(19,33)(24,39)(25,42)(31,46)(32,34)(40,47)(41,43)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26693);