Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #7262 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#7281 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #340 |
| commutator | C2×C8 | C42×C7 |
| Frattini, cosocle | C2×C4×C8 | C22×C7 |
| prime radical | C23×C7 | #103 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
226 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 2 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,12)(11,14)(13,15)(16,17,20,23,21,25,30,24)(18,19,26,28,22,29,27,31);(9,12)(10,15)(13,14)(16,18,19,24,20,27,28,25,21,22,29,23,30,26,31,17)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 269);