Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#123 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C23 |
| prime radical | C2×D4×C23 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ G | |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 368 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,27)(29,32)(30,34);(28,29)(30,33)(31,32)(34,35);(24,25)(26,27)(28,30,31,34)(29,33,32,35)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 158);