Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #6057⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #6057⋊D3 |
| Fitting, socle, Hall | C3×C52 ⋊ #41 |
| Sylow | C52 ⋊ #239 |
| Sylow | C3 ⋊ (D5⋊AGL(1,𝔽5))⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C3×C5⋊D5 | C23 |
| Fitting, socle, hypocenter | C3×C52 | #41 |
| LCS | G ▷ C3×C5⋊D5 ▷ C3×C52 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30 |
Polycyclic presentation:
2^4,3,5^2|b^2=d,c^2=d,b^a=bd,e^a=e^2,f^a=f^4,c^b=cd,f^b=g^4,g^b=f,f^c=f^3,g^c=g^2,f^d=f^4,g^d=g^424 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 966);