Finite Group DatabasebetaFinite Group Databasebeta| order | 1215 |
| isoclinism | isoclinic class of C34⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C32 |
| direct product | C3×C34⋊C5 |
| unambiguous semidirect product | C35⋊C5 |
| Fitting, socle, Sylow | C35 ⋊ C5 |
| derived | C34 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C34⋊C5 |
| commutator, cosocle, hypocenter | C34 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C35 | C5 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C3 | |
540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15 |
63 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1215, 69);