Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C22×C42 |
| direct product | C7×#14591 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C24 | C24×C7 |
| prime radical | C25×C7 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
1442 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)(8,9,11,10)(13,16)(14,18)(20,21,23,24)(22,25,26,27)(28,29,31,34)(30,33,35,32);(13,16)(17,19)(21,24)(22,26)(28,30,31,35)(29,32,34,33);(8,10,11,9)(12,13,15,16)(14,17,18,19)(20,21)(22,25)(23,24)(26,27)(28,30)(29,33)(31,35)(32,34);(12,14)(13,17)(15,18)(16,19)(20,22)(21,25)(23,26)(24,27)(28,29)(30,33)(31,34)(32,35)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 7579);