Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#400 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C23 |
| commutator, Frattini, cosocle | C23 | C23×C19 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1216 |
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)(26,30)(28,31)(32,33,35,37)(34,38,39,36);(21,23)(24,25,27,29)(26,31,30,28)(32,33)(34,38)(35,37)(36,39);(20,21)(22,23)(24,26)(25,28)(27,30)(29,31)(32,34,35,39)(33,36,37,38)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 81);