Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 13440 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C3×C5×C11 |
| multiplicative | (ℤ/1771)ˣ, (ℤ/2139)ˣ, (ℤ/2211)ˣ, (ℤ/2277)ˣ, (ℤ/2541)ˣ, (ℤ/2648)ˣ, (ℤ/2852)ˣ, (ℤ/2948)ˣ, (ℤ/3388)ˣ, (ℤ/3542)ˣ, (ℤ/3972)ˣ, (ℤ/4278)ˣ, (ℤ/4356)ˣ, (ℤ/4422)ˣ, (ℤ/4554)ˣ, (ℤ/5082)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
128 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 1320 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2)(7,8,9)(10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25);(3,4);(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, 181);