Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7×C8 · Schur multiplier (H2) = C25 |
| direct product | C7×#17858 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22×D4 |
| commutator | C4 | C23×C7×C8 |
| Frattini, cosocle | C42 | C24×C7 |
| socle | C22×C7 | C2×C4×D4 |
| prime radical | C2×C7×#135 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C7×#431 ◁ G | |
714 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,11,14,12,10,13,15)(16,17,22,27)(18,28,19,24)(20,26,21,25)(23,30,31,29);(16,18,22,19)(17,23,27,31)(20,29,21,30)(24,25,28,26);(8,10,11,15,12,9,13,14)(16,19,22,18)(17,24,27,28)(20,29,21,30)(23,25,31,26);(16,20,22,21)(17,25,27,26)(18,29,19,30)(23,28,31,24)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 10846);