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×#34439 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C23 | C25×C7 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
2278 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)(12,13,15,17)(14,18,19,16)(20,21)(22,26)(23,30)(24,25)(27,31)(28,34)(29,32)(33,35);(12,13,15,17)(14,16,19,18)(21,25)(26,32)(27,30)(33,34);(8,10,11,9)(12,13)(14,16)(15,17)(18,19)(20,22,24,29)(21,26,25,32)(23,28,31,35)(27,33,30,34);(12,14,15,19)(13,16,17,18)(20,21)(22,26)(23,27)(24,25)(28,33)(29,32)(30,31)(34,35);(20,23,24,31)(21,27,25,30)(22,28,29,35)(26,33,32,34)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27427);