Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#560 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
252 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,23)(17,22)(18,20)(19,25)(21,27)(24,28)(26,29);(14,16)(15,19)(17,25)(18,26)(20,28)(21,29)(22,23)(24,27);(15,20)(16,24)(19,23)(21,22)(25,26)(28,29);(15,21)(16,25)(19,28)(20,22)(23,29)(24,26)247 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1561);