Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13387 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C7×#3058 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C7×#131 ◁ G | |
428 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)(9,10)(12,13)(14,18)(15,19)(16,31)(17,22)(20,28)(21,29)(23,33)(24,41)(25,34)(26,35)(27,36)(30,38)(32,40)(37,43)(39,42);(8,9)(10,11)(12,14)(13,18)(15,27)(16,23)(17,26)(19,36)(20,39)(21,34)(22,35)(24,30)(25,29)(28,42)(31,33)(32,37)(38,41)(40,43);(8,10,11,9)(13,19)(14,23)(15,28)(16,29)(18,32)(20,21)(22,38)(24,27)(25,26)(30,43)(31,37)(33,41)(34,36)(35,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6375);