Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×#479 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C13 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ G | |
90 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)(14,15,17,19)(16,20,21,18)(22,23,25,27)(24,30,31,37)(26,34,33,29)(28,35,36,32);(14,16,17,21)(15,18,19,20)(23,27)(28,36)(29,34)(30,37);(22,24,25,31)(23,28,27,36)(26,35,33,32)(29,37,34,30)247 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 980);