Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#21429 |
| 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 | |
1010 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)(8,9)(10,13)(11,12)(14,15)(16,17,20,25,21,24,26,38)(18,22,29,34,28,35,32,39)(19,23,31,37,30,36,40,46)(27,33,42,45,41,44,43,47);(16,18,26,29,21,28,20,32)(17,22,25,39,24,35,38,34)(19,27,40,42,30,41,31,43)(23,33,37,47,36,44,46,45);(9,12)(13,15)(16,19,21,30)(17,23,24,36)(18,27,28,41)(20,31,26,40)(22,33,35,44)(25,37,38,46)(29,42,32,43)(34,45,39,47);(8,10,11,14)(9,13,12,15)(19,30)(23,36)(27,41)(31,40)(33,44)(37,46)(42,43)(45,47)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14417);