Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#34361 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C23 | C25×C7 |
| prime radical | C2×C7×#525 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
2458 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7)(8,9,10,11)(13,16)(14,18)(20,21)(22,25)(23,28)(24,29)(26,30)(27,32)(31,33)(34,35);(13,16)(17,19)(21,22)(23,30)(27,29)(31,35);(12,13)(14,17)(15,16)(18,19)(20,22,25,21)(23,28,30,26)(24,29,32,27)(31,34,35,33);(12,14)(13,17)(15,18)(16,19)(20,23)(21,26)(22,28)(24,31)(25,30)(27,33)(29,34)(32,35);(20,24,25,32)(21,27,22,29)(23,31,30,35)(26,33,28,34)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27349);