Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#23211 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C23×C7 | C23×C4 |
| prime radical | C22×C7×D4 | C2×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
852 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(9,11)(13,17)(18,19)(20,21,26,22,25,28,24,30)(23,27,31,29,32,35,33,34);(12,13)(14,18)(15,19)(16,17)(20,22,26,28,25,30,24,21)(23,29,31,35,32,34,33,27);(8,9,10,11)(12,14,16,15)(13,18,17,19)(20,23,25,32)(21,27,28,35)(22,29,30,34)(24,33,26,31);(12,15,16,14)(13,18,17,19)(20,24,25,26)(21,22,28,30)(23,31,32,33)(27,34,35,29)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16199);