Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60927 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#3062 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×#41 ◁ 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)(18,26)(19,30)(20,24)(21,35)(22,28)(23,33)(25,34)(27,43)(29,38)(31,47)(32,41)(36,40)(37,46)(39,44)(42,45);(8,9)(10,13)(11,12)(14,15)(16,18)(17,22)(19,31)(20,28)(21,29)(23,39)(24,26)(25,38)(27,32)(30,43)(33,46)(34,45)(35,42)(36,44)(37,40)(41,47);(9,12)(13,15)(16,19,20,32)(17,23,24,40)(18,27,28,31)(21,36,34,33)(22,37,26,39)(25,41,35,30)(29,46,45,44)(38,43,42,47);(8,10,11,14)(9,13,12,15)(17,24)(22,26)(23,40)(25,35)(30,41)(37,39)(38,42)(43,47);(18,28)(22,26)(27,31)(29,45)(37,39)(38,42)(43,47)(44,46)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53915);