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×#62020 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#3561 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#529 ◁ G | |
1772 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)(16,17,20,24)(18,26,28,22)(19,30,31,39)(21,34,33,25)(23,35,38,32)(27,42,43,47)(29,37,45,41)(36,44,40,46);(8,9)(10,13)(11,12)(14,15)(16,18)(17,22)(19,27)(20,28)(21,29)(23,36)(24,26)(25,37)(30,47)(31,43)(32,44)(33,45)(34,41)(35,46)(38,40)(39,42);(16,19,20,31)(17,23,24,38)(18,27,28,43)(21,35,33,32)(22,36,26,40)(25,39,34,30)(29,46,45,44)(37,42,41,47);(9,12)(13,15)(18,28)(22,26)(27,43)(29,45)(36,40)(37,41)(42,47)(44,46);(8,10,11,14)(9,13,12,15)(17,24)(18,28)(23,38)(25,34)(27,43)(29,45)(30,39)(44,46)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55008);