Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C7 · Schur multiplier (H2) = C26×C42 |
| direct product | C2×C7×#2375 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C24 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C23 | C25×C7 |
| prime radical | C22×C7×#120 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
4246 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2)(23,24,25,26,27,28,29);(3,4,5,6)(8,11)(9,13)(15,16)(17,21)(18,19)(20,22);(8,11)(12,14)(16,19)(17,22);(7,8)(9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22);(7,9)(8,12)(10,13)(11,14)(15,17)(16,20)(18,22)(19,21)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27326);