Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C2 |
| direct product | C23×#125 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C23 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ G | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(26,30)(28,31)(32,33,35,37)(34,36,38,39);(24,25,27,29)(26,28,30,31)(32,33)(34,36)(35,37)(38,39);(24,26)(25,28)(27,30)(29,31)(32,34,35,38)(33,36,37,39)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 160);