Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13313 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#13314 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #466 |
| 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 | |
536 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)(8,9)(10,11)(12,13,18,24)(14,25,29,38)(15,19,32,35)(16,23,17,22)(20,26,39,28)(21,31,34,30)(27,37,42,36)(33,41,40,43);(13,19)(14,26)(15,30)(16,17)(20,36)(21,22)(23,34)(24,35)(25,40)(27,42)(28,29)(31,32)(33,38)(37,39);(9,11)(12,14)(13,20)(15,27)(16,26)(17,28)(18,29)(19,33)(21,37)(22,38)(23,25)(24,39)(30,41)(31,43)(32,42)(34,36)(35,40)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6302);