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×#62821 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
7338 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)(18,27)(19,30)(20,21)(22,23)(24,28)(25,29)(26,31);(10,14)(13,15)(17,23)(18,28)(20,26)(25,30);(8,9)(10,13)(11,12)(14,15)(16,18)(17,24)(19,26)(20,29)(21,30)(22,28)(23,27)(25,31);(16,19,22,29)(17,25,23,30)(18,26,28,20)(21,24,31,27);(8,10)(9,13)(11,14)(12,15)(16,20,22,26)(17,21,23,31)(18,29,28,19)(24,30,27,25);(8,9)(10,13)(11,12)(14,15)(16,21)(17,26)(18,30)(19,24)(20,23)(22,31)(25,28)(27,29)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55809);