Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#413 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C22⋊C4 |
| commutator | C22 | C22×C4×C19 |
| Frattini, cosocle | C2×C4 | C23×C19 |
| socle | C2×C19 | C2×C22⋊C4 |
| prime radical | C2×#41×C19 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ G | |
150 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
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)(20,21,24,29,25,28,23,27)(22,30,31,35,32,26,33,34);(20,22)(21,26)(23,31)(24,33)(25,32)(27,34)(28,30)(29,35);(20,23,25,24)(21,27,28,29)(22,31,32,33)(26,34,30,35)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 94);