Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #3415 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#33382 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×D8 |
| commutator | C8 | C23×C4×C7 |
| Frattini, cosocle | C2×C8 | C24×C7 |
| prime radical | C2×C7×#578 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C7×#41 ◁ C2×C7×#131 ◁ G | |
1124 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9,10,11)(13,18)(15,25)(16,27)(19,31)(20,35)(21,32)(23,38)(24,37)(26,29)(28,30)(33,42)(34,43)(36,41)(39,40);(12,13,17,21)(14,19,22,33)(15,26,28,35)(16,29,27,20)(18,30,32,25)(23,39,36,43)(24,40,37,34)(31,41,42,38);(12,14)(13,19)(15,23)(16,24)(17,22)(18,31)(20,34)(21,33)(25,38)(26,39)(27,37)(28,36)(29,40)(30,41)(32,42)(35,43);(14,22)(19,33)(23,36)(24,37)(31,42)(34,40)(38,41)(39,43)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26370);