Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#399 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C23 |
| commutator, Frattini, cosocle | C23 | C23×C13 |
| prime radical | C24×C13 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
186 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,20,21)(24,28)(26,29);(15,17)(19,21)(22,23,25,27)(24,29,28,26);(14,15)(16,17)(18,19)(20,21)(22,24)(23,26)(25,28)(27,29)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 900);