Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4608 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C9×C16 |
| multiplicative | (ℤ/969)ˣ, (ℤ/1216)ˣ, (ℤ/1292)ˣ, (ℤ/1728)ˣ, (ℤ/1836)ˣ, (ℤ/1938)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C8 | C23×C3 |
| socle, prime radical | C23×C3 | C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
147 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 576 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(21,22,23,24,25,26,27,28,29);(17,18);(19,20)576 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 938);