Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#410 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C22⋊C4 |
| commutator | C22 | C22×C4×C13 |
| Frattini, cosocle | C23 | C23×C13 |
| socle | C2×C13 | C2×C22⋊C4 |
| prime radical | C2×C13×#41 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
158 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)(16,22,24,19)(17,20)(18,21)(23,28,29,26)(25,27);(14,16)(15,19)(17,23)(18,24)(20,26)(21,22)(25,29)(27,28);(14,17,18,25)(15,20,21,27)(16,23,24,29)(19,26,22,28)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 911);