Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11677 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C2×C4 |
| direct product | C7×#13289 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#102 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C23×C7 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,12)(13,15)(16,17,21,28,23,29,22,27)(18,30,35,47,36,46,34,42)(19,37,31,25,38,26,20,39)(24,41,43,33,45,32,44,40);(9,12)(13,14)(16,18,31,33,22,35,19,32,23,36,20,40,21,34,38,41)(17,24,26,46,28,44,39,47,29,45,37,30,27,43,25,42);(8,10,11,15)(9,13,12,14)(16,19,21,31,23,38,22,20)(17,25,27,37,29,39,28,26)(18,32,34,33,36,41,35,40)(24,42,43,30,45,47,44,46)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6277);