Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60717 |
| 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 ◁ C4×C7×#41 ◁ G | |
1870 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)(8,9)(10,13)(11,12)(14,15)(16,17)(18,28)(19,31)(20,24)(21,26)(22,27)(23,37)(25,35)(29,43)(30,40)(32,45)(33,41)(34,46)(36,39)(38,47)(42,44);(9,12)(13,15)(16,18,22,20)(17,24,27,28)(19,29,34,32)(21,36,23,30)(25,38,41,42)(26,40,37,39)(31,45,46,43)(33,47,35,44);(16,19,23,35,22,34,21,33)(17,25,26,31,27,41,37,46)(18,29,30,44,20,32,36,47)(24,38,40,45,28,42,39,43);(8,10,11,14)(9,13,12,15)(16,20,22,18)(17,24,27,28)(19,32,34,29)(21,30,23,36)(25,38,41,42)(26,40,37,39)(31,45,46,43)(33,44,35,47);(16,21,22,23)(17,26,27,37)(18,30,20,36)(19,33,34,35)(24,39,28,40)(25,31,41,46)(29,44,32,47)(38,43,42,45)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53705);