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) = C22 |
| direct product | C13×#357 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D8 |
| commutator | C8 | C2×C4×C13 |
| Frattini, cosocle | C2×C8 | C22×C13 |
| prime radical | C2×C13×D8 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C4×C13 ◁ C2×C8×C13 ◁ G | |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(18,19)(20,23)(21,30)(22,26)(24,27)(25,28)(29,32)(31,33);(19,23)(20,27)(21,28)(24,25)(26,32)(29,33)(30,31)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 162);