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×#60315 |
| 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 | |
1816 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)(16,17,20,25,21,23,32,36)(18,22,28,35,26,33,40,44)(19,29,30,43,31,24,37,38)(27,41,42,47,39,34,45,46);(8,10)(9,12)(11,15)(13,14)(16,18)(17,22)(19,27)(20,28)(21,26)(23,33)(24,34)(25,35)(29,41)(30,42)(31,39)(32,40)(36,44)(37,45)(38,46)(43,47);(10,15)(12,14)(17,23)(18,26)(24,29)(25,36)(27,39)(28,40)(38,43)(42,45);(9,13)(12,14)(18,26)(22,33)(27,39)(28,40)(34,41)(35,44)(42,45)(46,47);(16,19,20,30,21,31,32,37)(17,24,25,38,23,29,36,43)(18,27,28,42,26,39,40,45)(22,34,35,46,33,41,44,47)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53303);