Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60460 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60720 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#535 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×#41 ◁ 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)(18,22,27,36)(19,29,32,46)(20,33,34,24)(23,38,40,31)(26,41,30,45)(28,44,43,37)(35,47,39,42);(9,12)(13,15)(16,18)(17,22)(19,30)(20,28)(21,27)(23,39)(24,37)(25,36)(26,32)(29,45)(31,47)(33,44)(34,43)(35,40)(38,42)(41,46);(16,19,20,31,21,32,34,38)(17,23,24,29,25,40,33,46)(18,26,28,42,27,30,43,47)(22,35,37,41,36,39,44,45);(8,10,11,14)(9,13,12,15)(16,18)(17,22)(19,26)(20,28)(21,27)(23,35)(24,37)(25,36)(29,41)(30,32)(31,42)(33,44)(34,43)(38,47)(39,40)(45,46);(18,27)(22,36)(26,30)(28,43)(35,39)(37,44)(41,45)(42,47)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53708);