Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17405 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25×C4 |
| direct product | C7×#21751 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C24 | C24×C7 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C7×Q8 ◁ G | |
1294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,17)(18,22)(19,29,31,23)(20,24)(21,25)(26,40,42,34)(27,35)(28,36)(30,43,45,37)(32,38)(33,39)(41,47,44,46);(8,10)(9,12)(11,15)(13,14)(16,18,21,28)(17,22,25,36)(19,26,31,42)(20,32,33,27)(23,34,29,40)(24,38,39,35)(30,44,45,41)(37,47,43,46);(10,15)(12,14)(16,19)(17,23)(18,26)(20,30)(21,31)(22,34)(24,37)(25,29)(27,41)(28,42)(32,44)(33,45)(35,46)(36,40)(38,47)(39,43);(9,13)(12,14)(16,20,21,33)(17,24,25,39)(18,27,28,32)(19,30,31,45)(22,35,36,38)(23,37,29,43)(26,41,42,44)(34,46,40,47)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14739);