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×#34395 |
| 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 | |
1990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7)(8,9,10,11)(13,17)(14,20)(19,24)(21,26)(28,29,32,33)(30,36,37,34)(31,39,40,35)(38,41,43,42);(13,17)(18,23)(19,24)(25,27)(29,33)(30,37)(35,39)(38,43);(12,13,16,17)(14,18,20,23)(15,19,22,24)(21,25,26,27)(28,29)(30,34)(31,35)(32,33)(36,37)(38,41)(39,40)(42,43);(12,14)(13,18)(15,21)(16,20)(17,23)(19,25)(22,26)(24,27)(28,30,32,37)(29,34,33,36)(31,38,40,43)(35,41,39,42);(12,15,16,22)(13,19,17,24)(14,21,20,26)(18,25,23,27)(28,31,32,40)(29,35,33,39)(30,38,37,43)(34,41,36,42)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27383);