Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18992 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18994 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3153 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
936 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)(10,14)(13,15)(16,17)(18,28)(19,32)(20,27)(21,26)(22,25)(23,30)(24,33)(29,37)(31,40)(34,41)(35,38)(36,39)(42,44)(43,46)(45,47);(10,14)(12,15)(16,18)(17,23)(19,29)(20,35)(21,30)(22,31)(24,37)(25,38)(26,40)(27,28)(32,46)(33,44)(34,45)(36,43)(39,47)(41,42);(8,9)(10,15)(11,13)(12,14)(16,19,22,34)(17,24,25,39)(18,29,31,45)(20,33,21,36)(23,37,38,47)(26,32,27,41)(28,42,40,46)(30,43,35,44);(17,25)(23,38)(24,39)(26,27)(28,40)(32,41)(37,47)(42,46)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11982);