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×#22949 |
| 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)(18,23,29,37,30,38,28,44)(19,31,33,24,32,40,35,39)(27,41,43,36,42,47,45,46);(8,9)(10,13)(11,12)(14,15)(16,18,21,29,22,30,20,28)(17,23,25,37,26,38,34,44)(19,27,33,43,32,42,35,45)(24,36,40,47,39,46,31,41);(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)(28,45)(29,43)(30,42)(31,34)(37,47)(38,46)(41,44);(9,12)(13,15)(19,32)(24,39)(27,42)(31,40)(33,35)(36,46)(41,47)(43,45)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 15937);