Finite Group DatabasebetaFinite Group Databasebeta| order | 2340 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1728 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C5×C9×C13 |
| multiplicative | (ℤ/2489)ˣ, (ℤ/3513)ˣ, (ℤ/3537)ˣ, (ℤ/4684)ˣ, (ℤ/4978)ˣ, (ℤ/7026)ˣ, (ℤ/7074)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C22×C3×C5×C13 |
| socle, prime radical | C22×C3×C5×C13 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 2340 |
A minimal faithful permutation representation — 2 generators on 31 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);(3,4)2340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2340, 13);