Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4×#120 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#36609 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C2×C7×#127 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1938 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)(8,9)(10,13)(11,14)(12,15)(16,17)(18,21)(19,20)(22,23)(24,25,29,27)(26,30,28,31);(8,10,11,15)(9,12,14,13)(17,20)(21,22)(24,25,29,27)(26,31,28,30);(8,9,11,14)(10,13,15,12)(16,17)(18,22)(19,20)(21,23)(24,26,29,28)(25,30,27,31);(8,9)(10,12)(11,14)(13,15)(16,18,19,23)(17,21,20,22)(24,27,29,25)(26,30,28,31);(8,10)(9,13)(11,15)(12,14)(16,17)(18,22)(19,20)(21,23)(24,28,29,26)(25,31,27,30)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29597);