Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#19761 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3358 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C42×C7 ◁ G | |
694 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,12)(11,14)(13,15)(17,21)(19,27)(22,30)(23,28)(24,31)(25,29);(16,17,20,23)(18,24,26,30)(19,28,27,21)(22,29,31,25);(9,12)(10,15)(13,14);(16,18,20,26)(17,22,23,31)(19,29,27,25)(21,30,28,24)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12749);