Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#430 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C2×D4 |
| commutator | C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C4 | C23×C13 |
| socle | C2×C13 | C2×C4⋊C4 |
| prime radical | C23×C13 | Q8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,21,19,22,17,27)(16,23,26,28,24,29,25,20);(14,16,17,25,19,24,18,26)(15,20,21,23,22,28,27,29);(16,24)(20,28)(23,29)(25,26)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 931);