Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61197 |
| 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 ◁ C7×#525 ◁ G | |
2046 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)(8,9,11,13)(10,14,15,12)(16,17)(18,23)(19,32)(20,25)(21,26)(22,27)(24,33)(28,42)(29,37)(30,41)(31,38)(34,39)(35,40)(36,43)(44,47)(45,46);(8,10)(9,12)(11,15)(13,14)(16,18,22,31)(17,23,27,38)(19,28,34,45)(20,29,21,30)(24,36,40,47)(25,37,26,41)(32,42,39,46)(33,43,35,44);(16,19)(17,24)(18,28)(20,33)(21,35)(22,34)(23,36)(25,39)(26,32)(27,40)(29,43)(30,44)(31,45)(37,46)(38,47)(41,42);(10,15)(12,14)(16,20,22,21)(17,25,27,26)(18,29,31,30)(19,33,34,35)(23,37,38,41)(24,39,40,32)(28,43,45,44)(36,46,47,42);(16,20,22,21)(17,26,27,25)(18,30,31,29)(19,33,34,35)(23,37,38,41)(24,32,40,39)(28,44,45,43)(36,46,47,42)385 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54185);