Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #20671 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#33427 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#117 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C2×C8 | C24×C7 |
| socle | C2×C7 | C2×#432 |
| prime radical | C24×C7 | M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C7×#405 ◁ G | |
524 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,11,16,12,17,24,32,13,14,22,27,25,28,37,39)(10,18,20,34,21,26,36,31,19,33,23,38,35,15,29,30);(9,14)(11,22)(15,26)(17,28)(18,33)(20,23)(24,37)(29,36);(8,10)(9,15,14,26)(11,23)(12,21)(13,19)(16,31,27,30)(17,18,28,33)(20,22)(24,29)(25,35)(32,38,39,34)(36,37);(10,19)(15,26)(18,33)(20,23)(21,35)(29,36)(30,31)(34,38)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26415);