Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#400 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C23 |
| commutator, Frattini, cosocle | C23 | C23×C13 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(20,24)(22,25)(26,27,29,31)(28,32,33,30);(15,17)(18,19,21,23)(20,25,24,22)(26,27)(28,32)(29,31)(30,33);(14,15)(16,17)(18,20)(19,22)(21,24)(23,25)(26,28,29,33)(27,30,31,32)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 901);