Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C52 ⋊ C2×Q8 |
| Sylow | C52 ⋊ C2×Dic6 |
| Sylow | C3 ⋊ #87872 |
184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3,5^2|a^2=d,c^2=d,c^a=cd,e^a=e^2,f^a=f^4,f^b=f^4,g^b=g^4102 conjugacy classes — view the full character table.
| maximal subgroup of | #72229438, #72229591, #72229652, … |
| maximal normal subgroup of | #72229438, #72229591, #72229652, … |
| maximal quotient of | C3×#11925650, #72231364 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 860);