Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#368 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | D8 |
| commutator | C8 | C2×C4×C13 |
| Frattini, cosocle | C2×C8 | C22×C13 |
| socle | C2×C13 | #107 |
| prime radical | C22×C13 | Q16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C2×C4×C13 ◁ C2×C8×C13 ◁ G | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 2 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,23,20,24,19,34)(16,25,28,40,30,41,29,44)(17,31,32,38,33,45,26,22)(21,35,36,43,37,42,39,27);(14,16,26,42,19,29,33,43,20,30,32,35,18,28,17,27)(15,21,31,40,23,36,38,41,24,37,45,44,34,39,22,25)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 173);