Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | Dic3⋊#1039 |
| Hall | C3×C52 ⋊ C4⋊C4 |
| Sylow | C52 ⋊ Dic3⋊C4 |
| Sylow | C3 ⋊ C4⋊#1039 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D3×C5⋊D5 |
| commutator | C2×C3×C52 | C2×C4 |
| Fitting, socle, prime radical, cosocle | C22×C3×C52 | C22 |
| hypocenter | C3×C52 | C4⋊C4 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C22 | |
208 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1200 |
Polycyclic presentation:
2^4,3,5^2|a^2=d,b^2=c,b^a=bc,f^a=f^4,g^a=g^4,e^b=e^2162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 333);