Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62861 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6854 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 6 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,11,13)(10,12,14,15)(16,17)(18,23)(19,29)(20,24)(21,35)(22,26)(25,36)(27,37)(28,31)(30,32)(33,45)(34,40)(38,42)(39,46)(41,43)(44,47);(8,9)(10,12)(11,13)(14,15)(16,18,22,29)(17,23,26,19)(20,32,34,27)(21,28,36,42)(24,30,40,37)(25,38,35,31)(33,44,46,41)(39,43,45,47);(16,19)(17,18)(20,30)(21,31)(22,23)(24,27)(25,28)(26,29)(32,40)(33,43)(34,37)(35,42)(36,38)(39,41)(44,45)(46,47);(16,17)(18,23)(19,29)(20,24)(21,25)(22,26)(27,37)(28,38)(30,32)(31,42)(33,39)(34,40)(35,36)(41,47)(43,44)(45,46);(16,20,22,34)(17,24,26,40)(18,27,29,32)(19,30,23,37)(21,33,36,46)(25,39,35,45)(28,41,42,44)(31,43,38,47);(8,10,11,14)(9,12,13,15)(16,21)(17,25)(18,28)(19,31)(20,33)(22,36)(23,38)(24,39)(26,35)(27,41)(29,42)(30,43)(32,44)(34,46)(37,47)(40,45)574 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55849);