Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×C3×C52 ⋊ C4 |
| Hall | C3×C52 ⋊ C22⋊C4 |
| Sylow | C52 ⋊ #217 |
| Sylow | C3 ⋊ C22⋊#1043 |
272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
Polycyclic presentation:
2^4,3,5^2|a^2=c,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 | D4×C3⋊#1043, C2×#11925533, C3×#11925533, … |
| maximal normal subgroup of | D4×C3⋊#1043, C2×#11925533, C3×#11925533, … |
| maximal quotient of | C2×#11925533, C3×#11925533, #72229571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 743);