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×#62830 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
7264 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 6 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,12)(11,15)(13,14)(17,21)(19,26)(22,27)(25,30);(9,14)(10,15)(18,24)(22,27)(25,30)(29,31);(8,10,13,15)(9,11,14,12)(16,17,20,21)(18,22,24,27)(19,23,26,28)(25,29,30,31);(8,11,13,12)(9,10,14,15);(8,9)(10,11)(12,15)(13,14)(16,18)(17,22)(19,25)(20,24)(21,27)(23,29)(26,30)(28,31);(8,12,13,11)(9,15,14,10)(16,19)(17,23)(18,25)(20,26)(21,28)(22,29)(24,30)(27,31)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55818);