Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C4 |
| direct product | C13×#488 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C13 |
| prime radical | C2×D4×C13 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ G | |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,18)(20,21)(22,23)(24,32)(25,28)(26,36)(27,31)(29,34)(30,33)(35,37);(15,18)(19,21)(22,24,33,35,27,34,26,25)(23,28,36,29,31,37,30,32);(14,16,17,20)(15,19,18,21)(22,25,26,34,27,35,33,24)(23,29,30,28,31,32,36,37)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 989);