Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of Dic30 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×C4⋊Dic15 |
| unambiguous semidirect product | C4⋊(C5×Dic15) |
| Hall | C3×C52 ⋊ C4⋊C4 |
| Sylow | C52 ⋊ C4⋊Dic3 |
| Sylow | C3 ⋊ C5×C4⋊Dic5 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 442);