Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C16 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×#674 |
| derived | C5 ⋊ C3×C5×C16 |
| Hall | C3×C52 ⋊ C16 |
| Sylow | C52 ⋊ C3×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4×C5 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C3×C5×C16 |
| Frattini | C4 | C3×C5×AGL(1,𝔽5) |
| Fitting | C3×C4×C52 | C4 |
| socle, prime radical | C2×C3×C52 | C8 |
| cosocle | #168 | C2×C3×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C3×C4×C5 | |
46 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 240 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 260);