Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23532 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1326 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)(10,11)(12,13)(14,24)(15,29)(16,22)(17,21)(18,23)(19,26)(20,33)(25,34)(27,36)(28,35)(30,42)(31,38)(32,37)(39,41)(40,43);(12,14,18,28)(13,19,23,36)(15,30,31,25)(16,27,17,26)(20,34,37,42)(21,35,22,24)(29,39,38,43)(32,40,33,41);(9,11)(12,15,16,32,18,31,17,33)(13,20,21,38,23,37,22,29)(14,25,26,40,28,30,27,41)(19,34,24,39,36,42,35,43);(15,31)(20,37)(25,30)(29,38)(32,33)(34,42)(39,43)(40,41)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16520);