Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60454 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60705 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#3455 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C7×#117 ◁ G | |
1846 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)(16,17,21,25)(18,22,27,35)(19,29,30,44)(20,32,33,24)(23,37,38,31)(26,39,40,47)(28,43,42,36)(34,45,46,41);(9,12)(13,15)(16,18,21,27)(17,22,25,35)(19,26,30,40)(20,28,33,42)(23,34,38,46)(24,36,32,43)(29,39,44,47)(31,41,37,45);(16,19,20,31,21,30,33,37)(17,23,24,29,25,38,32,44)(18,26,28,41,27,40,42,45)(22,34,36,39,35,46,43,47);(8,10,11,14)(9,13,12,15)(18,27)(22,35)(26,40)(28,42)(34,46)(36,43)(39,47)(41,45);(19,30)(23,38)(26,40)(29,44)(31,37)(34,46)(39,47)(41,45)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53693);