Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6670 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 6 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,18)(11,16)(12,14)(13,17)(15,22)(19,31)(20,27)(21,32)(23,30)(24,26)(25,34)(28,37)(29,35)(33,39)(36,38);(9,14)(10,19)(11,23)(16,29)(17,27)(21,36)(22,34)(24,35)(26,30)(28,32)(33,37)(38,39);(8,10,20,34)(9,15,27,31)(11,21,35,36)(12,19,13,22)(14,25,17,18)(16,28,29,39)(23,37,24,33)(26,38,30,32);(9,14)(15,25)(16,26)(17,27)(18,31)(28,38)(29,30)(32,39);(8,11,12,24)(9,16,14,26)(10,21,19,33)(13,23,20,35)(15,28,25,38)(17,30,27,29)(18,32,31,39)(22,37,34,36);(9,17)(14,27)(15,18)(16,30)(25,31)(26,29)(28,32)(38,39)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55814);