Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Fitting | C2×C3×C4×C52 ⋊ C2 |
| Hall | C3×C52 ⋊ C22⋊C4 |
| Sylow | C52 ⋊ (C2×D3)⋊C4 |
| Sylow | C3 ⋊ #87808 |
272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
Polycyclic presentation:
2^4,3,5^2|b^2=c,b^a=bd,e^a=e^2,f^a=f^4,g^a=g^4306 conjugacy classes — view the full character table.
| maximal subgroup of | #72229762, (C2×D3)⋊C4×C5⋊D5, #72231367, … |
| maximal normal subgroup of | #72229762, (C2×D3)⋊C4×C5⋊D5, #72231367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 459);