Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61609 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61862 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#449 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#533 ◁ G | |
1614 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 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)(24,25,29,34)(26,36,38,31)(27,40,42,49)(28,35,30,33)(32,44,47,41)(37,51,52,55)(39,46,43,48)(45,54,50,53);(8,10,12,18)(9,13,15,16)(11,19,20,17)(14,22,23,21)(24,26,29,38)(25,31,34,36)(27,37,42,52)(28,43,30,39)(32,45,47,50)(33,48,35,46)(40,55,49,51)(41,54,44,53);(24,27)(25,32)(26,37)(28,41)(29,42)(30,44)(31,45)(33,40)(34,47)(35,49)(36,50)(38,52)(39,53)(43,54)(46,51)(48,55);(8,11,12,20)(9,14,15,23)(10,17,18,19)(13,21,16,22)(26,38)(31,36)(37,52)(39,43)(45,50)(46,48)(51,55)(53,54);(9,15)(13,16)(14,23)(21,22)(24,28,29,30)(25,33,34,35)(26,39,38,43)(27,41,42,44)(31,46,36,48)(32,40,47,49)(37,53,52,54)(45,51,50,55)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54850);