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×#62828 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6636 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)(10,12)(11,19)(13,14)(15,17)(16,21)(18,22)(20,23)(25,29)(27,34)(30,35)(33,38);(9,14)(10,17)(16,19)(18,23)(26,32)(30,35)(33,38)(37,39);(8,10,13,17)(9,15,14,12)(11,18,21,23)(16,22,19,20)(24,25,28,29)(26,30,32,35)(27,31,34,36)(33,37,38,39);(8,11)(9,16)(10,18)(12,20)(13,21)(14,19)(15,22)(17,23);(8,9)(10,15)(11,16)(12,17)(13,14)(18,22)(19,21)(20,23)(24,26)(25,30)(27,33)(28,32)(29,35)(31,37)(34,38)(36,39);(8,12,13,15)(9,17,14,10)(11,20,21,22)(16,23,19,18)(24,27)(25,31)(26,33)(28,34)(29,36)(30,37)(32,38)(35,39)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55816);