Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#23047 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#41 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
840 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9,11,10)(12,13,17,22,18,23,16,21)(14,24,27,19,28,35,26,36)(15,29,32,38,33,20,31,39)(25,40,41,43,42,37,30,34);(8,10,11,9)(12,14)(13,19)(15,30)(16,27)(17,26)(18,28)(20,37)(21,35)(22,24)(23,36)(25,31)(29,40)(32,42)(33,41)(34,38)(39,43);(12,14)(13,19)(15,25)(16,26)(17,27)(18,28)(20,34)(21,24)(22,35)(23,36)(29,43)(30,31)(32,41)(33,42)(37,38)(39,40);(12,15,16,31,18,33,17,32)(13,20,21,38,23,29,22,39)(14,25,26,30,28,42,27,41)(19,34,24,37,36,43,35,40)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16035);