Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C16 · Schur multiplier (H2) = C2 |
| direct product | C13×C4⋊C16 |
| unambiguous semidirect product | C4⋊(C13×C16) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C13 | C22 |
| commutator | C2 | C2×C13×C16 |
| Frattini, cosocle | C2×C8 | C22×C13 |
| socle, prime radical | C22×C13 | C2×C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C13 ◁ G | |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,20,23,21,24,26,29,22,25,27,30,28,31,32,33);(14,15,16,17)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 168);