Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C4 |
| direct product | C13×#490 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C13 |
| prime radical | C13×#127 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ G | |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 416 |
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)(16,19)(17,18)(20,21)(23,28)(24,29)(25,26);(15,18)(19,21)(22,23,25,28,27,29,26,24);(14,16,17,20)(15,19,18,21)(22,24,25,23,27,28,26,29)208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 991);