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×#62819 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
7242 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 6 generators on 31 points:
(1,2,3,4,5,6,7)(9,12)(13,15)(16,17)(18,24)(19,21)(20,27)(22,26)(23,28)(25,29)(30,31);(10,14)(13,15)(16,18,21,26)(17,22,19,24)(20,25,28,31)(23,29,27,30);(8,9)(10,13)(11,12)(14,15)(16,19,21,17)(18,22,26,24)(20,27,28,23)(25,29,31,30);(16,20)(17,23)(18,25)(19,27)(21,28)(22,29)(24,30)(26,31);(8,10)(9,13)(11,14)(12,15)(16,18)(17,24)(19,22)(20,25)(21,26)(23,30)(27,29)(28,31);(8,9)(10,13)(11,12)(14,15)(16,20)(17,23)(18,25)(19,27)(21,28)(22,29)(24,30)(26,31)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55807);