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×#16484 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C7 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
1050 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(9,11)(12,13,15,17)(14,16,18,19)(20,21,24,25)(22,23,27,26)(28,29,31,34)(30,33,35,32);(14,18)(16,19)(21,25)(22,27)(28,30,31,35)(29,32,34,33);(12,14)(13,16)(15,18)(17,19)(20,22,24,27)(21,26,25,23)(28,30)(29,33)(31,35)(32,34);(8,9)(10,11)(12,13)(14,16)(15,17)(18,19)(20,23,24,26)(21,22,25,27)(28,29)(30,32)(31,34)(33,35)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 9472);