Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #36702 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#36753 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1588 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(10,14)(13,15)(16,17,20,21)(18,23,19,22)(24,25,27,29)(26,30,31,28);(9,12)(13,15)(17,21)(22,23);(8,9)(10,13)(11,12)(14,15)(16,18,20,19)(17,22,21,23)(24,26,27,31)(25,28,29,30);(8,9)(10,13)(11,12)(14,15)(16,17)(18,22)(19,23)(20,21);(8,10)(9,13)(11,14)(12,15)(16,19,20,18)(17,23,21,22)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29741);