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×#62036 |
| 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 | |
1766 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)(16,17,22,27)(18,23,30,38)(19,32,34,41)(20,26,21,25)(24,35,40,33)(28,42,44,47)(29,39,31,37)(36,45,46,43);(8,9)(10,13)(11,12)(14,15)(16,18)(17,23)(19,28)(20,29)(21,31)(22,30)(24,36)(25,37)(26,39)(27,38)(32,42)(33,43)(34,44)(35,45)(40,46)(41,47);(16,19,22,34)(17,24,27,40)(18,28,30,44)(20,33,21,35)(23,36,38,46)(25,32,26,41)(29,43,31,45)(37,42,39,47);(9,12)(13,15)(16,20,22,21)(17,25,27,26)(18,29,30,31)(19,33,34,35)(23,37,38,39)(24,32,40,41)(28,43,44,45)(36,42,46,47);(8,10,11,14)(9,13,12,15)(18,30)(23,38)(28,44)(29,31)(36,46)(37,39)(42,47)(43,45)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55024);