Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61629 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#62069 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#529 ◁ G | |
1782 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)(9,12)(10,14)(16,17)(18,27)(19,32)(20,25)(21,26)(22,35)(23,30)(24,33)(28,43)(29,42)(31,38)(34,39)(36,40)(37,46)(41,44)(45,47);(8,9)(10,13)(11,12)(14,15)(16,18,21,30)(17,23,26,27)(19,28,34,45)(20,29,22,31)(24,37,40,41)(25,38,35,42)(32,47,39,43)(33,44,36,46);(16,19)(17,24)(18,28)(20,33)(21,34)(22,36)(23,37)(25,39)(26,40)(27,41)(29,44)(30,45)(31,46)(32,35)(38,43)(42,47);(9,12)(13,15)(16,20,21,22)(17,25,26,35)(18,29,30,31)(19,33,34,36)(23,38,27,42)(24,39,40,32)(28,44,45,46)(37,43,41,47);(8,10,11,14)(9,13,12,15)(17,26)(18,30)(24,40)(25,35)(28,45)(29,31)(32,39)(44,46)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55057);