Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61269 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#525 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#525 ◁ G | |
1750 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)(8,9,12,11)(10,14,15,13)(16,17)(18,23)(19,30)(20,26)(21,34)(22,25)(24,31)(27,42)(28,38)(29,37)(32,41)(33,39)(35,40)(36,44)(43,46)(45,47);(8,10)(9,13)(11,14)(12,15)(16,18,22,29)(17,23,25,37)(19,27,32,45)(20,33,21,28)(24,36,40,46)(26,39,34,38)(30,42,41,47)(31,44,35,43);(8,11,12,9)(10,14,15,13)(16,19)(17,24)(18,27)(20,31)(21,35)(22,32)(23,36)(25,40)(26,41)(28,43)(29,45)(30,34)(33,44)(37,46)(38,42)(39,47);(10,15)(13,14)(17,25)(23,37)(24,40)(26,34)(30,41)(36,46)(38,39)(42,47);(16,20,22,21)(17,26,25,34)(18,28,29,33)(19,31,32,35)(23,38,37,39)(24,41,40,30)(27,43,45,44)(36,42,46,47)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54257);