Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60318 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C25 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C2×C4 | C25×C7 |
| socle | C22×C7 | C24×C4 |
| prime radical | C7×#3529 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ G | |
1812 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,17,20,25,21,26,33,41)(18,22,29,35,27,23,36,38)(19,30,31,44,32,24,39,40)(28,37,43,47,42,34,45,46);(8,10)(9,12)(11,15)(13,14)(16,18)(17,22)(19,28)(20,29)(21,27)(23,26)(24,34)(25,35)(30,37)(31,43)(32,42)(33,36)(38,41)(39,45)(40,46)(44,47);(10,15)(12,14)(16,18)(17,23)(19,28)(20,29)(21,27)(22,26)(24,37)(25,38)(30,34)(31,43)(32,42)(33,36)(35,41)(39,45)(40,47)(44,46);(9,13)(12,14)(18,27)(22,23)(28,42)(29,36)(34,37)(35,38)(43,45)(46,47);(16,19,20,31,21,32,33,39)(17,24,25,40,26,30,41,44)(18,28,29,43,27,42,36,45)(22,34,35,46,23,37,38,47)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53306);