Finite Group DatabasebetaFinite Group Databasebeta| order | 1116 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1080 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C9×C31 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C22×C3×C31 |
| socle, prime radical | C22×C3×C31 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 1116 |
A minimal faithful permutation representation — 2 generators on 44 points:
(1,2)(5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44);(3,4)1116 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1116, 15);