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×#60270 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C25 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C2×C4 | C25×C7 |
| socle | C22×C7 | C24×C4 |
| prime radical | C7×#3455 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ G | |
1786 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(16,17,20,25,21,24,31,37)(18,22,28,33,27,34,40,44)(19,23,30,36,29,35,41,45)(26,32,39,43,38,42,46,47);(8,9)(10,13)(11,12)(14,15)(16,18)(17,22)(19,26)(20,28)(21,27)(23,32)(24,34)(25,33)(29,38)(30,39)(31,40)(35,42)(36,43)(37,44)(41,46)(45,47);(9,12)(13,15)(16,19)(17,23)(18,26)(20,30)(21,29)(22,32)(24,35)(25,36)(27,38)(28,39)(31,41)(33,43)(34,42)(37,45)(40,46)(44,47);(8,10,11,14)(9,13,12,15)(19,29)(23,35)(26,38)(30,41)(32,42)(36,45)(39,46)(43,47);(17,24)(18,27)(23,35)(25,37)(26,38)(28,40)(36,45)(39,46)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53258);