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×#34452 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C23 | C25×C7 |
| prime radical | C2×C7×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
2066 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7)(8,9,11,10)(12,13)(14,15)(16,17)(18,19)(21,25)(22,28)(27,32)(29,34);(13,17)(14,18)(21,25)(26,31)(27,32)(33,35);(8,10,11,9)(20,21)(22,26)(23,27)(24,25)(28,31)(29,33)(30,32)(34,35);(12,14,16,18)(13,15,17,19)(20,22,24,28)(21,26,25,31)(23,29,30,34)(27,33,32,35);(12,15)(13,18)(14,17)(16,19)(20,23,24,30)(21,27,25,32)(22,29,28,34)(26,33,31,35)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27440);