Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62850 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6846 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 6 generators on 47 points:
(1,2,3,4,5,6,7)(9,12)(13,15)(17,22)(20,32)(23,26)(24,33)(28,42)(31,43)(35,38)(41,47);(8,9)(10,13)(11,12)(14,15)(19,30)(24,33)(27,40)(31,43)(35,38)(37,44)(41,47)(45,46);(16,17,21,22)(18,26,29,23)(19,24,30,33)(20,25,32,34)(27,38,40,35)(28,39,42,36)(31,37,43,44)(41,46,47,45);(16,18,21,29)(17,23,22,26)(19,27,30,40)(20,28,32,42)(24,35,33,38)(25,36,34,39)(31,41,43,47)(37,45,44,46);(8,10,11,14)(9,13,12,15)(16,19)(17,24)(18,27)(20,31)(21,30)(22,33)(23,35)(25,37)(26,38)(28,41)(29,40)(32,43)(34,44)(36,45)(39,46)(42,47);(16,20)(17,25)(18,28)(19,31)(21,32)(22,34)(23,36)(24,37)(26,39)(27,41)(29,42)(30,43)(33,44)(35,45)(38,46)(40,47)574 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55838);