Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#338 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C42 |
| commutator | C4 | C42×C19 |
| Frattini, cosocle | C22×C4 | C22×C19 |
| socle | C2×C19 | #95 |
| prime radical | C23×C19 | Q8 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ G | |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,27,25,28,24,33)(22,29,31,26,32,34,30,35);(20,22,24,31,25,32,23,30)(21,26,27,29,28,35,33,34)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 19);