Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C7×#1831 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C7 | C23 |
| commutator | C22 | C23×C7×C8 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle, prime radical | C24×C7 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C7 ◁ G | |
1246 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2)(23,24,25,26,27,28,29);(4,5)(7,8)(9,12)(10,11)(13,14)(15,16,17,19,18,20,21,22);(3,4,6,5)(8,11)(12,14);(3,5,6,4)(7,9,10,13)(8,12,11,14)784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13738);