Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#13282 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C2×D8 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7)(8,9,10,11)(12,13)(14,18)(15,16)(17,19)(21,27)(22,23)(24,25)(28,33)(29,30)(31,34)(32,35);(9,11)(13,16)(17,18)(20,21,28,34,25,31,23,27,26,32,22,29,24,30,33,35);(12,14,15,19)(13,17,16,18)(20,22,25,33,26,28,24,23)(21,29,31,35,32,34,30,27)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6270);