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×#401 |
| 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 | |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(16,20)(18,21)(23,26)(27,28)(30,31,33,35)(32,36,37,34);(14,15,17,19)(16,21,20,18)(22,23,25,26)(24,28,29,27)(30,31)(32,36)(33,35)(34,37);(14,16)(15,18)(17,20)(19,21)(22,24,25,29)(23,27,26,28)(30,32,33,37)(31,34,35,36)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 902);