Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61264 |
| 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 | |
1764 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)(20,25)(21,34)(22,26)(24,31)(27,42)(28,37)(29,39)(32,40)(33,38)(35,41)(36,44)(43,46)(45,47);(8,10)(9,13)(11,14)(12,15)(16,18,22,29)(17,23,26,39)(19,27,32,45)(20,33,21,28)(24,36,41,46)(25,38,34,37)(30,42,40,47)(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)(37,42)(38,47)(39,46);(10,15)(13,14);(16,20,22,21)(17,25,26,34)(18,28,29,33)(19,31,32,35)(23,37,39,38)(24,40,41,30)(27,43,45,44)(36,42,46,47)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54252);