Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#11393 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #120 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| socle | C22×C7 | #379 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C23×C4×C7 ◁ G | |
850 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(16,17,21,25,22,26,20,33)(18,27,29,23,30,38,34,37)(19,24,31,40,32,41,35,39)(28,43,46,47,45,42,44,36);(8,9,11,13)(10,14,15,12)(16,18)(17,23)(19,28)(20,34)(21,29)(22,30)(24,36)(25,38)(26,37)(27,33)(31,46)(32,45)(35,44)(39,42)(40,43)(41,47);(8,10,11,15)(9,12,13,14)(16,19)(17,24)(18,28)(20,35)(21,31)(22,32)(23,36)(25,40)(26,41)(27,42)(29,46)(30,45)(33,39)(34,44)(37,47)(38,43)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4381);