Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C7×#1834 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C7 | C2×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ C22×C42×C7 ◁ G | |
1182 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);(3,4,5,6)(7,8)(9,12)(10,11)(13,14)(16,21)(17,22)(18,19);(8,11)(12,14)(15,16,19,17,20,22,18,21);(7,9,10,13)(8,12,11,14)(15,17,18,16,20,21,19,22)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13746);