Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C16 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×#672 |
| derived | C5 ⋊ C3×C5×C16 |
| Hall | C3×C52 ⋊ C16 |
| Sylow | C52 ⋊ C3×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C8 | D5 |
| commutator, hypocenter | C5 | C3×C5×C16 |
| Frattini | C8 | C3×C5×D5 |
| Fitting | C3×C52×C8 | C2 |
| socle, prime radical | C2×C3×C52 | C8 |
| cosocle | C5×C8 | C2×C3×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C3×C5×C8 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 186);