Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #16249 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#16580 |
| 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)(22,23,27,26)(29,30)(31,35);(14,19)(17,18)(21,25)(22,27)(28,29,32,30)(31,33,35,34);(12,14)(13,17)(15,18)(16,19)(20,22,24,27)(21,26,25,23)(28,30,32,29)(31,33,35,34);(8,9)(10,11)(12,15,16,13)(14,18,19,17)(20,23,24,26)(21,22,25,27)(28,31,32,35)(29,33,30,34)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 9568);