Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×C5×Dic5 |
| derived | C5 ⋊ C22×C3×C4×C5 |
| Hall | C3×C52 ⋊ C22×C4 |
| Sylow | C52 ⋊ C22×C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3×C5 | D5 |
| commutator, hypocenter | C5 | C22×C3×C4×C5 |
| Frattini | C2 | C22×C3×C5×D5 |
| Fitting, socle, prime radical | C23×C3×C52 | C2 |
| cosocle | C2×C5 | C23×C3×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C23×C3×C5 | |
280 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, 893);