Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13398 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13399 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #481 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C24×C7 | SD16 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C22×C7×M16 ◁ G | |
406 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)(12,13,17,21)(14,22,23,40)(15,26,27,43)(16,31,29,20)(18,33,34,24)(19,36,37,30)(25,38,32,41)(28,35,42,39);(8,9)(10,11)(15,27)(19,37)(22,40)(24,33)(26,43)(28,42)(30,36)(38,41);(9,11)(12,14,16,32,17,23,29,25)(13,18,20,39,21,34,31,35)(15,28,30,33,27,42,36,24)(19,38,26,40,37,41,43,22)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6387);