Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17405 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#21883 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C7×#117 ◁ G | |
954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(16,17,21,25,20,24,34,41)(18,26,29,43,28,22,36,38)(19,30,33,42,32,23,35,40)(27,37,44,46,31,39,45,47);(8,9)(10,13)(11,12)(14,15)(16,18)(17,22)(19,31)(20,28)(21,29)(23,39)(24,26)(25,38)(27,32)(30,37)(33,45)(34,36)(35,44)(40,47)(41,43)(42,46);(9,12)(13,15)(16,19,20,32)(17,23,24,30)(18,27,28,31)(21,35,34,33)(22,37,26,39)(25,42,41,40)(29,45,36,44)(38,47,43,46);(8,10,11,14)(9,13,12,15)(17,24)(18,28)(23,30)(25,41)(27,31)(29,36)(40,42)(44,45)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14871);