Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C42 |
| commutator | C4 | C42×C13 |
| Frattini, cosocle | C22×C4 | C22×C13 |
| socle | C2×C13 | #95 |
| prime radical | C23×C13 | D4 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ G | |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,22,24,28)(17,20)(18,21)(19,23,26,29)(25,27);(14,16)(15,19,21,26)(17,23)(18,24)(20,22,27,28)(25,29)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 142);