Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60372 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60499 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C2×C7×2−1+4 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×#41 ◁ G | |
1970 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)(8,9,11,13)(10,14,15,12)(16,17,20,22)(18,26,28,39)(19,24,30,36)(21,33,32,25)(23,34,35,29)(27,40,41,47)(31,44,43,38)(37,45,46,42);(8,10,11,15)(9,12,13,14)(17,22)(23,35)(24,36)(25,33)(26,39)(37,46)(38,44)(40,47);(16,18,20,28)(17,23,22,35)(19,27,30,41)(21,34,32,29)(24,37,36,46)(25,39,33,26)(31,45,43,42)(38,47,44,40);(16,19)(17,24)(18,27)(20,30)(21,31)(22,36)(23,37)(25,38)(26,40)(28,41)(29,42)(32,43)(33,44)(34,45)(35,46)(39,47);(19,30)(24,36)(27,41)(31,43)(37,46)(38,44)(40,47)(42,45)427 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53487);