Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61609 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#62012 |
| 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 | |
1792 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)(9,12)(10,14)(16,17)(18,23)(19,31)(20,25)(21,34)(22,26)(24,32)(27,41)(28,37)(29,38)(30,44)(33,39)(35,40)(36,42)(43,46)(45,47);(8,9)(10,13)(11,12)(14,15)(16,18,22,29)(17,23,26,38)(19,27,33,43)(20,28,21,30)(24,36,40,47)(25,37,34,44)(31,41,39,46)(32,42,35,45);(16,19)(17,24)(18,27)(20,32)(21,35)(22,33)(23,36)(25,39)(26,40)(28,42)(29,43)(30,45)(31,34)(37,46)(38,47)(41,44);(9,12)(13,15)(16,20,22,21)(17,25,26,34)(18,28,29,30)(19,32,33,35)(23,37,38,44)(24,39,40,31)(27,42,43,45)(36,46,47,41);(8,10,11,14)(9,13,12,15)(18,29)(23,38)(27,43)(28,30)(36,47)(37,44)(41,46)(42,45)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55000);