Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#341 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | D4 |
| commutator | C4 | C42×C13 |
| Frattini, cosocle | C22×C4 | C22×C13 |
| socle | C22×C13 | C4⋊C4 |
| prime radical | C23×C13 | Q8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C22×C4×C13 ◁ G | |
90 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)(18,19,21,26,23,27,22,25)(20,28,29,24,31,32,30,33);(15,17)(18,20,22,30,23,31,21,29)(19,24,26,32,27,33,25,28)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 146);