Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊#1035 |
| unambiguous semidirect product | (C2×#1035)⋊D3 |
| Hall | C3×C25 ⋊ C22⋊C4 |
| Sylow | C25 ⋊ (C2×D3)⋊C4 |
| Sylow | C3 ⋊ C22⋊#1035 |
102 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 102 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 300 |
Polycyclic presentation:
2^4,3,5^2|a^2=c,f^5=g,b^a=bd,f^a=f^2g,g^a=g^2,e^b=e^2,f^c=f^4g^4,g^c=g^454 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 95);