Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C52 ⋊ C2×Q8 |
| Sylow | C52 ⋊ D3×Q8 |
| Sylow | C3 ⋊ #87872 |
184 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 52 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=d,b^2=d,c^2=d,c^a=cd,e^a=e^2,f^a=f^4,c^b=cd,g^b=g^4111 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#87872, #72230616, #72230622, … |
| maximal normal subgroup of | D3×#87872, #72230616, #72230622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 836);