Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×#329 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22⋊C4 |
| commutator | C2×C4 | C2×C4×C13 |
| Frattini, cosocle | C42 | C22×C13 |
| prime radical | C2×D4×C13 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ G | |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,19,17,18,20,21)(23,26,27,28);(15,18)(16,20)(22,23)(24,28)(25,27)(26,29)247 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 134);