Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C52 ⋊ M16 |
| Sylow | C52 ⋊ #208 |
| Sylow | C3 ⋊ #87853 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3,5^2|a^2=c,c^2=d,b^a=bd,e^a=e^2,f^a=f^2,g^a=g^4,f^c=f^4126 conjugacy classes — view the full character table.
| maximal subgroup of | #72229770, #72231061, D3×#87853, … |
| maximal normal subgroup of | #72229770, #72231061, D3×#87853, … |
| maximal quotient of | C3×#11925546 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 756);