Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#22951 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C2×C4×D4 |
| prime radical | C7×#525 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C2×C7×C22⋊C8 ◁ G | |
730 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(9,12)(13,15)(16,17,21,25,22,26,20,34)(18,23,30,38,28,37,29,44)(19,31,33,24,32,40,35,39)(27,41,42,36,43,46,45,47);(8,9)(10,13)(11,12)(14,15)(16,18,21,30,22,28,20,29)(17,23,25,38,26,37,34,44)(19,27,33,42,32,43,35,45)(24,36,40,46,39,47,31,41);(8,10,11,14)(9,13,12,15)(16,19)(17,24)(18,27)(20,35)(21,33)(22,32)(23,36)(25,40)(26,39)(28,43)(29,45)(30,42)(31,34)(37,47)(38,46)(41,44);(9,12)(13,15)(18,28)(19,32)(23,37)(24,39)(29,30)(31,40)(33,35)(38,44)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 15939);