Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#21077 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9,11,10)(12,13)(14,23)(15,27)(16,21)(17,32)(18,22)(19,25)(20,30)(24,38)(26,34)(28,42)(29,36)(31,35)(33,43)(37,40)(39,41);(8,10,11,9)(12,14,17,25,18,26,16,31)(13,19,21,23,22,35,32,34)(15,24,29,39,30,40,28,43)(20,33,36,37,27,41,42,38);(12,15,17,29,18,30,16,28)(13,20,21,36,22,27,32,42)(14,24,25,39,26,40,31,43)(19,33,23,37,35,41,34,38);(12,16,18,17)(13,21,22,32)(14,25,26,31)(15,28,30,29)(19,34,35,23)(20,36,27,42)(24,39,40,43)(33,38,41,37)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14065);