Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#13329 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C22×C7×D8 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
578 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(16,17,21,26)(18,27,30,45)(19,23,34,41)(20,35,33,25)(22,37,39,28)(24,42,40,32)(29,46,36,43)(31,44,47,38);(9,11)(12,13)(14,15)(16,18,21,30)(17,22,26,39)(19,31,34,47)(20,36,33,29)(23,27,41,45)(24,43,40,46)(25,44,35,38)(28,42,37,32);(13,15)(17,23)(19,32)(20,33)(22,27)(24,25)(26,41)(28,31)(29,36)(34,42)(35,40)(37,47)(38,46)(39,45)(43,44)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6317);