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×#62833 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
7050 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)(9,12)(13,15)(17,22)(18,26)(19,29)(25,30);(10,14)(13,15)(16,17,21,22)(18,27,26,23)(19,24,29,31)(20,30,28,25);(8,9)(10,13)(11,12)(14,15)(16,18,21,26)(17,23,22,27)(19,28,29,20)(24,30,31,25);(16,19)(17,24)(18,28)(20,26)(21,29)(22,31)(23,30)(25,27);(8,10,11,14)(9,13,12,15)(16,20,21,28)(17,25,22,30)(18,19,26,29)(23,24,27,31);(8,9)(10,13)(11,12)(14,15)(16,19)(17,24)(18,28)(20,26)(21,29)(22,31)(23,30)(25,27)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55821);