Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62862 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62886 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6918 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)(10,14)(11,12)(13,15)(17,22)(18,26)(20,33)(24,30)(28,38)(31,44)(36,41)(45,47);(9,12)(13,14)(16,17,21,22)(18,23,26,27)(19,30,32,24)(20,25,33,34)(28,40,38,35)(29,36,39,41)(31,43,44,37)(42,47,46,45);(8,9)(10,13)(11,12)(14,15)(16,17)(18,27)(19,24)(20,25)(21,22)(23,26)(28,40)(29,41)(30,32)(31,37)(33,34)(35,38)(36,39)(42,47)(43,44)(45,46);(8,10)(9,13)(11,15)(12,14)(16,18)(17,23)(19,28)(20,29)(21,26)(22,27)(24,35)(25,36)(30,40)(31,42)(32,38)(33,39)(34,41)(37,45)(43,47)(44,46);(16,19,21,32)(17,24,22,30)(18,28,26,38)(20,31,33,44)(23,35,27,40)(25,37,34,43)(29,42,39,46)(36,45,41,47);(16,20)(17,25)(18,29)(19,31)(21,33)(22,34)(23,36)(24,37)(26,39)(27,41)(28,42)(30,43)(32,44)(35,45)(38,46)(40,47)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55874);