Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62817 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
9494 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 6 generators on 23 points:
(1,2,3,4,5,6,7)(8,9)(10,16)(11,15)(12,14)(13,17)(18,20)(19,22)(21,23);(8,10)(9,13)(11,17)(12,18)(14,21)(15,16)(19,23)(20,22);(9,14)(10,17)(13,20)(15,22)(16,21)(18,23);(9,15)(13,16)(14,22)(20,21);(10,18)(13,21)(16,20)(17,23);(9,14)(13,21)(15,22)(16,20)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55805);