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×#62824 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
7330 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)(8,9)(10,11)(12,13)(14,15)(17,21)(19,26)(22,27)(25,30);(9,13)(11,14)(18,24)(22,27)(25,30)(29,31);(8,9,12,13)(10,14,15,11)(16,17,20,21)(18,22,24,27)(19,23,26,28)(25,29,30,31);(8,10)(9,14)(11,13)(12,15);(8,11,12,14)(9,10,13,15)(16,18)(17,22)(19,25)(20,24)(21,27)(23,29)(26,30)(28,31);(8,10)(9,14)(11,13)(12,15)(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, 55812);