Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18973 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
818 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7)(9,14)(10,17)(11,12)(16,20)(18,19)(21,22)(24,25,29,33)(26,34,37,47)(27,31,38,45)(28,40,42,32)(30,41,44,36)(35,48,49,55)(39,52,51,46)(43,53,54,50);(8,9,13,16)(10,15,19,23)(11,14,12,20)(17,21,18,22)(24,26,29,37)(25,30,33,44)(27,35,38,49)(28,41,42,36)(31,43,45,54)(32,47,40,34)(39,53,51,50)(46,55,52,48);(8,10,13,19)(9,15,16,23)(11,17,12,18)(14,21,20,22)(24,27,29,38)(25,31,33,45)(26,35,37,49)(28,39,42,51)(30,43,44,54)(32,46,40,52)(34,48,47,55)(36,50,41,53);(8,11,13,12)(9,14,16,20)(10,18,19,17)(15,22,23,21)(27,38)(31,45)(35,49)(39,51)(43,54)(46,52)(48,55)(50,53)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11961);