Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#544 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C19 |
| prime radical | C23×C19 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ G | |
206 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 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)(22,26)(23,25)(24,27)(28,29,31,33)(30,34,35,32);(20,21,23,25)(22,24,27,26);(20,21)(22,24)(23,25)(26,27)(28,30,31,35)(29,32,33,34);(20,22)(21,24)(23,27)(25,26)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 225);