Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#36652 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| socle | C23×C7 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
2570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13)(14,16)(15,17)(18,19)(20,21)(22,26)(23,27)(24,25)(28,31)(29,33)(30,32)(34,35);(14,18)(16,19)(21,25)(26,31)(27,32)(33,35);(9,11)(12,14)(13,16)(15,18)(17,19)(20,22)(21,26)(23,29)(24,28)(25,31)(27,33)(30,34)(32,35);(13,17)(14,18)(22,28)(26,31)(29,34)(33,35);(20,23,24,30)(21,27,25,32)(22,29,28,34)(26,33,31,35)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29640);