Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic3⋊#1035 |
| Hall | C3×C25 ⋊ C4⋊C4 |
| Sylow | C25 ⋊ Dic3⋊C4 |
| Sylow | C3 ⋊ C4⋊#1035 |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 300 |
Polycyclic presentation:
2^4,3,5^2|a^2=c,b^2=d,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, 92);