Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62862 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62873 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 6 generators on 55 points:
(1,2,3,4,5,6,7)(8,9)(10,16)(11,14)(12,15)(13,18)(17,22)(19,21)(20,23)(25,30)(28,40)(31,34)(32,41)(36,50)(39,51)(43,46)(49,55);(8,9,12,15)(10,13,18,16)(11,14,19,21)(17,20,23,22)(27,38)(32,41)(35,48)(39,51)(43,46)(45,52)(49,55)(53,54);(8,9)(10,13)(11,14)(12,15)(16,18)(17,20)(19,21)(22,23)(24,25,29,30)(26,34,37,31)(27,32,38,41)(28,33,40,42)(35,46,48,43)(36,47,50,44)(39,45,51,52)(49,54,55,53);(8,10)(9,13)(11,17)(12,18)(14,20)(15,16)(19,23)(21,22)(24,26,29,37)(25,31,30,34)(27,35,38,48)(28,36,40,50)(32,43,41,46)(33,44,42,47)(39,49,51,55)(45,53,52,54);(8,11,12,19)(9,14,15,21)(10,17,18,23)(13,20,16,22)(24,27)(25,32)(26,35)(28,39)(29,38)(30,41)(31,43)(33,45)(34,46)(36,49)(37,48)(40,51)(42,52)(44,53)(47,54)(50,55);(24,28)(25,33)(26,36)(27,39)(29,40)(30,42)(31,44)(32,45)(34,47)(35,49)(37,50)(38,51)(41,52)(43,53)(46,54)(48,55)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55861);