Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60685 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| socle | C22×C7 | C23×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C2×C7×#117 ◁ G | |
1878 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)(10,13)(11,12)(14,15)(16,17)(18,23)(19,31)(20,25)(21,36)(22,26)(24,34)(27,42)(28,38)(29,39)(30,45)(32,46)(33,41)(35,47)(37,44)(40,43);(9,12)(13,15)(16,18)(17,23)(19,32)(20,29)(21,30)(22,28)(24,40)(25,39)(26,38)(27,35)(31,46)(33,44)(34,43)(36,45)(37,41)(42,47);(16,19,21,34,22,35,20,33)(17,24,25,31,26,41,36,47)(18,27,30,44,28,32,29,43)(23,37,39,42,38,40,45,46);(8,10,11,14)(9,13,12,15)(18,28)(23,38)(27,32)(29,30)(37,40)(39,45)(42,46)(43,44);(16,20,22,21)(17,25,26,36)(18,29,28,30)(19,33,35,34)(23,39,38,45)(24,31,41,47)(27,43,32,44)(37,42,40,46)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53673);