Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#13320 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C2×C7×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C7×#131 ◁ G | |
540 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(13,19)(14,24)(15,27)(16,17)(20,36)(21,28)(22,34)(23,35)(25,29)(26,32)(30,31)(33,38)(37,40)(39,42);(8,9)(10,11)(12,13,18,23)(14,20,26,39)(15,28,31,34)(16,22,17,21)(19,30,35,27)(24,40,32,38)(25,42,29,36)(33,41,37,43);(9,11)(12,14)(13,20)(15,29)(16,32)(17,24)(18,26)(19,33)(21,40)(22,38)(23,39)(25,31)(27,43)(28,36)(30,41)(34,42)(35,37)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6308);