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⋊#1042 |
146 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3,5^2|a^2=c,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 | D5×#6763, D15×C22⋊AGL(1,𝔽5), D3×C22⋊#1042 |
| maximal normal subgroup of | D5×#6763, D15×C22⋊AGL(1,𝔽5), D3×C22⋊#1042 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 757);