Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#17880 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C42 | C24×C7 |
| socle | C22×C7 | C2×C4×D4 |
| prime radical | C23×C7 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C7×#431 ◁ G | |
626 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,11,10,12,13,15,14)(16,17)(18,26)(19,23)(20,32)(21,24)(22,28)(25,34)(27,40)(29,39)(30,38)(31,44)(33,36)(35,42)(37,43)(41,47)(45,46);(16,18,21,29)(17,22,24,36)(19,27,30,41)(20,33,34,28)(23,35,38,46)(25,39,32,26)(31,45,43,42)(37,47,44,40);(8,10,11,13,12,14,15,9)(16,19,21,30)(17,23,24,38)(18,27,29,41)(20,31,34,43)(22,35,36,46)(25,37,32,44)(26,40,39,47)(28,42,33,45);(17,24)(19,30)(22,36)(25,32)(26,39)(27,41)(31,43)(42,45)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 10868);