Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1655 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#8912 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | #120 |
| commutator | C42 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
412 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)(8,9,11,10)(13,16)(14,18)(17,19)(20,21,26,31)(22,32,23,34)(24,30,25,29)(27,35,28,33);(8,10,11,9)(14,18)(16,19)(20,22,26,23)(21,27,31,28)(24,35,25,33)(29,34,30,32);(12,13)(14,19)(15,17)(16,18)(20,23,26,22)(21,28,31,27)(24,35,25,33)(29,34,30,32)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1900);