Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 120952258560 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C215 |
| abelian | C26×C9 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C26×C3 |
| socle, prime radical | C26×C3 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8475 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 576 |
A minimal faithful permutation representation — 6 generators on 21 points:
(1,2)(13,14,15,16,17,18,19,20,21);(3,4);(5,6);(7,8);(9,10);(11,12)576 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8268);