Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10012 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10013 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| socle | C22×C7 | #392 |
| prime radical | C7×#3100 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C2×C42×C7 ◁ G | |
598 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(13,15)(16,17)(18,24)(19,27)(20,23)(21,25)(22,29)(26,31)(28,30);(8,9,11,13)(10,15,14,12)(16,18,20,26)(17,21,23,30)(19,28,29,25)(22,31,27,24);(8,9)(10,15)(11,13)(12,14)(21,30)(24,31)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3001);