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×#62879 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 6 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,18)(12,13)(15,19)(16,20)(17,23)(21,22)(24,25,28,31)(26,29,34,32)(27,35,36,30)(33,38,39,37);(10,16)(14,20)(17,22)(21,23)(24,25)(26,32)(27,30)(28,31)(29,34)(33,38)(35,36)(37,39);(9,13)(14,20)(15,18)(21,23)(24,26)(25,29)(27,33)(28,34)(30,37)(31,32)(35,38)(36,39);(8,9)(10,14)(11,15)(12,13)(16,20)(17,21)(18,19)(22,23)(24,27,28,36)(25,30,31,35)(26,33,34,39)(29,37,32,38);(8,10,12,16)(9,14,13,20)(11,17,19,22)(15,21,18,23);(8,11)(9,15)(10,17)(12,19)(13,18)(14,21)(16,22)(20,23)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55867);