Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C3⋊#1043) |
| Fitting | C3×C4×C52 ⋊ C4 |
| Hall | C3×C52 ⋊ C4⋊C4 |
| Sylow | C52 ⋊ C4⋊Dic3 |
| Sylow | C3 ⋊ C4⋊#1043 |
208 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
Polycyclic presentation:
2^4,3,5^2|a^2=c,b^2=d,b^a=bd,e^a=e^2,f^a=f^2,g^a=g^2,f^c=f^4,g^c=g^490 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4⋊(C3⋊#1043), D4×C3⋊#1043, D3×C4⋊#1043, … |
| maximal normal subgroup of | C2×C4⋊(C3⋊#1043), D4×C3⋊#1043, D3×C4⋊#1043, … |
| maximal quotient of | C2×C4⋊(C3⋊#1043), #72229544, #72229694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 740);