Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60993 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×#41 ◁ G | |
1718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,16)(11,15)(12,14)(13,17)(18,22)(19,21)(20,23)(24,25,28,31)(26,33,36,39)(27,32,29,37)(30,38,34,35);(8,10)(9,13)(11,18)(12,17)(14,16)(15,20)(19,23)(21,22)(24,25)(26,34)(27,37)(28,31)(29,32)(30,36)(33,38)(35,39);(10,17)(13,16)(18,23)(20,22)(24,26,28,36)(25,30,31,34)(27,35,29,38)(32,39,37,33);(9,14)(13,16)(15,21)(20,22)(25,31)(30,34)(32,37)(33,39);(8,11,12,19)(9,15,14,21)(10,18,17,23)(13,20,16,22)(24,27,28,29)(25,32,31,37)(26,35,36,38)(30,39,34,33)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53981);