Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of AGL(1,𝔽25) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #87822⋊C3 |
| derived, Sylow | C52 ⋊ C3×C16 |
| Hall | #87822 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽25) |
| commutator, hypocenter | C52 | C3×C16 |
| Fitting, socle | C2×C52 | C3×C8 |
| prime radical | C2×C52⋊C3 | C8 |
| cosocle | #6033 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2,3,2^3,5^2|a^2=c,c^2=d,d^2=e,f^a=f^3g^3,g^a=f^3g^2,f^b=g^3,g^b=f^3g^4,f^c=f^3,g^c=g^3,f^d=f^4,g^d=g^450 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 486);