Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#11893 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#102 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C7×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ C23×C7×C8 ◁ G | |
400 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,14,15,12)(11,13)(16,17,20,26,22,28,21,27)(18,29,32,45,34,46,33,43)(19,35,37,25,39,44,38,24)(23,36,40,31,42,47,41,30);(8,10)(9,12)(11,15)(13,14)(16,18)(17,23)(19,36)(20,33)(21,32)(22,34)(24,43)(25,45)(26,41)(27,40)(28,42)(29,44)(30,37)(31,38)(35,46)(39,47);(10,15)(12,14)(16,19,20,37,22,39,21,38)(17,24,27,44,28,25,26,35)(18,30,32,36,34,31,33,47)(23,29,41,43,42,46,40,45)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4881);