Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 640 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C4×C5×C11 |
| multiplicative | (ℤ/1403)ˣ, (ℤ/1573)ˣ, (ℤ/1655)ˣ, (ℤ/1675)ˣ, (ℤ/1983)ˣ, (ℤ/2644)ˣ, (ℤ/2806)ˣ, (ℤ/3146)ˣ, (ℤ/3310)ˣ, (ℤ/3350)ˣ, (ℤ/3966)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C3×C5×C11 |
| socle, prime radical | C22×C3×C5×C11 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 1320 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3,4)(7,8,9)(10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25);(5,6)1320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 130);