Finite Group DatabasebetaFinite Group Databasebeta| order | 750 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2976000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C53 |
| abelian | C2×C3×C53 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
256 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 750 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2)(3,4,5)(6,7,8,9,10);(11,12,13,14,15);(16,17,18,19,20)750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(750, 39);