Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of Dic30 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#6710 |
| Hall | C3×C52 ⋊ M16 |
| Sylow | C52 ⋊ #208 |
| Sylow | C3 ⋊ C5×#681 |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72229453, C5×D3×#681, #72230510, … |
| maximal normal subgroup of | #72229453, C5×D3×#681, #72230510, … |
| maximal quotient of | C3×C5×#6710 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 439);