Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1685 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C4 |
| direct product | C7×#9587 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #121 |
| commutator | C42 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| socle | C22×C7 | #388 |
| prime radical | C23×C7 | #126 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C2×C42×C7 ◁ G | |
282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(9,13)(10,16)(11,19)(14,22)(15,21)(17,20)(24,25,28,32,29,33,27,30)(26,34,37,31,35,38,36,39);(8,9,11,13,12,15,19,21)(10,17,18,22,16,14,23,20)(25,30,33,32)(26,35)(31,38,39,34)(36,37);(8,10,11,18,12,16,19,23)(9,14,13,20,15,17,21,22)(24,26,27,36,29,35,28,37)(25,31,32,38,33,39,30,34)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2575);