Finite Group DatabasebetaFinite Group Databasebeta| order | 1260 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6912 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C22×C32×C5×C7 |
| multiplicative | (ℤ/1333)ˣ, (ℤ/1477)ˣ, (ℤ/1519)ˣ, (ℤ/1899)ˣ, (ℤ/2666)ˣ, (ℤ/2954)ˣ, (ℤ/3038)ˣ, (ℤ/3798)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 1260 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,2)(5,6,7)(11,12,13,14,15)(16,17,18,19,20,21,22);(3,4)(8,9,10)1260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1260, 131);