Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19733 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#19738 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
670 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(10,16)(11,18)(13,19)(15,21)(17,22)(20,23)(24,25,29,32)(26,33,31,28)(27,35,36,34)(30,38,39,37);(8,9)(10,13)(11,15)(12,14)(16,19)(17,20)(18,21)(22,23)(24,26,28,25,29,31,33,32)(27,34,37,30,36,35,38,39);(8,10,11,16,12,17,18,22)(9,13,15,19,14,20,21,23)(24,27,33,38,29,36,28,37)(25,30,26,34,32,39,31,35);(9,14)(13,20)(15,21)(19,23)(27,36)(30,39)(34,35)(37,38)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12726);