Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61286 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#532 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#532 ◁ G | |
1754 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,12,11)(10,14,15,13)(16,17)(18,22)(19,24)(20,23)(21,25)(26,32)(27,34)(28,36)(29,33)(30,39)(31,37)(35,42)(38,43)(40,44)(41,45)(46,47);(8,10)(9,13)(11,14)(12,15)(16,18,21,28)(17,22,25,36)(19,27,30,41)(20,29,32,42)(23,33,26,35)(24,34,39,45)(31,40,43,47)(37,44,38,46);(8,11,12,9)(10,14,15,13)(17,23)(20,32)(22,33)(24,37)(25,26)(29,42)(31,43)(34,44)(35,36)(38,39)(40,47)(45,46);(10,15)(13,14)(16,19)(17,24)(18,27)(20,31)(21,30)(22,34)(23,37)(25,39)(26,38)(28,41)(29,40)(32,43)(33,44)(35,46)(36,45)(42,47);(17,25)(18,28)(19,30)(23,26)(29,42)(31,43)(34,45)(44,46)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54274);