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×#13337 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C2×C7×#509 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C7×#405 ◁ G | |
554 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)(13,20)(14,26)(15,31)(16,34)(17,18)(21,38)(22,25)(23,32)(24,35)(28,36)(29,33)(30,42)(37,39)(41,43);(8,9)(10,11)(12,13,19,25)(14,27,30,40)(15,32,16,35)(17,24,18,23)(20,34,22,31)(21,29,38,28)(26,39,42,43)(33,41,36,37);(9,11)(12,14)(13,21)(15,33)(16,36)(17,29)(18,28)(19,30)(20,37)(22,41)(23,40)(24,27)(25,38)(26,34)(31,42)(32,43)(35,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6325);