Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #16249 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C2×C42 |
| direct product | C7×#16582 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| prime radical | C25×C7 | C23 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
1246 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)(12,13,16,15)(14,18,19,17)(20,21,24,25)(22,26,27,23)(28,29,31,33)(30,32,34,35);(14,19)(17,18)(21,25)(22,27)(28,30,31,34)(29,32,33,35);(12,14)(13,17)(15,18)(16,19)(20,22)(21,26)(23,25)(24,27)(28,30)(29,32)(31,34)(33,35);(8,9)(10,11)(12,15,16,13)(14,18,19,17)(20,23,24,26)(21,27,25,22)(28,29)(30,32)(31,33)(34,35)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 9570);