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×#62890 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6276 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)(8,9,13,14)(10,11,16,19)(12,15,20,21)(17,18,22,23)(24,25,30,34)(26,35,31,27)(28,32,42,48)(29,43,44,33)(36,46,40,38)(37,39,45,49)(41,53,54,47)(50,51,52,55);(9,14)(10,16)(15,21)(17,22)(24,26,30,31)(25,27,34,35)(28,40,42,36)(29,37,44,45)(32,46,48,38)(33,39,43,49)(41,52,54,50)(47,55,53,51);(8,10)(9,11)(12,17)(13,16)(14,19)(15,18)(20,22)(21,23)(24,26)(25,27)(28,36)(29,37)(30,31)(32,38)(33,39)(34,35)(40,42)(41,50)(43,49)(44,45)(46,48)(47,51)(52,54)(53,55);(8,11)(9,10)(12,18)(13,19)(14,16)(15,17)(20,23)(21,22)(24,27)(25,31)(26,34)(28,38)(29,39)(30,35)(32,40)(33,45)(36,48)(37,43)(41,51)(42,46)(44,49)(47,52)(50,53)(54,55);(24,28,30,42)(25,32,34,48)(26,36,31,40)(27,38,35,46)(29,41,44,54)(33,47,43,53)(37,50,45,52)(39,51,49,55);(8,12,13,20)(9,15,14,21)(10,17,16,22)(11,18,19,23)(24,29,30,44)(25,33,34,43)(26,37,31,45)(27,39,35,49)(28,41,42,54)(32,47,48,53)(36,50,40,52)(38,51,46,55)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55878);