Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#21547 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C2×C4×D4 |
| prime radical | C7×#3050 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C22×C7×M16 ◁ G | |
906 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)(10,11)(12,13,17,21,18,22,16,32)(14,23,26,34,27,39,25,19)(15,20,31,37,29,36,30,43)(24,38,41,35,28,42,40,33);(12,14,16,25,18,27,17,26)(13,19,21,23,22,34,32,39)(15,28,30,41,29,24,31,40)(20,35,37,42,36,33,43,38);(9,11)(15,29)(20,36)(24,28)(30,31)(33,35)(37,43)(38,42)(40,41);(12,15,17,31,18,29,16,30)(13,20,21,37,22,36,32,43)(14,24,26,41,27,28,25,40)(19,33,23,38,34,35,39,42)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14535);