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×#62867 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6758 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)(15,20)(19,28)(21,32)(22,31)(23,26)(24,27)(25,33)(29,35)(30,37)(34,39)(36,38);(9,14)(10,19)(11,22)(16,30)(17,27)(20,33)(21,36)(23,37)(26,31)(29,32)(34,35)(38,39);(8,10)(9,15)(11,21)(12,19)(13,20)(14,25)(16,29)(17,18)(22,35)(23,34)(24,33)(26,38)(27,28)(30,39)(31,32)(36,37);(9,14)(10,20)(15,28)(16,26)(17,27)(18,25)(19,33)(21,35)(29,39)(30,31)(32,38)(34,36);(8,11,12,23)(9,16,14,26)(10,21,19,34)(13,22,24,37)(15,29,25,38)(17,31,27,30)(18,32,28,39)(20,35,33,36);(9,17)(14,27)(15,18)(16,31)(25,28)(26,30)(29,32)(38,39)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55855);