Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#33703 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C7 |
| prime radical | C2×C7×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#117 ◁ C7×#405 ◁ G | |
570 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)(16,17,23,28)(18,29,31,30)(19,35,25,21)(20,36,38,26)(22,39,37,27)(24,40,41,32)(33,43,46,44)(34,42,47,45);(9,12)(13,15)(16,18,21,33,22,34,20,32,23,31,35,46,37,47,38,40)(17,24,26,42,27,43,25,29,28,41,36,45,39,44,19,30);(8,10,11,14)(9,13,12,15)(16,19,20,27,37,36,21,17,23,25,38,39,22,26,35,28)(18,30,32,43,47,45,33,24,31,29,40,44,34,42,46,41);(18,31)(24,41)(29,30)(32,40)(33,46)(34,47)(42,45)(43,44)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26691);