Finite Group DatabasebetaFinite Group Databasebeta| order | 3615 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C241⋊C3 |
| unambiguous semidirect product | (C5×C241)⋊C3 |
| Fitting, socle, Hall | C5×C241 ⋊ C3 |
| derived, Sylow | C241 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C241⋊C3 |
| commutator, cosocle, hypocenter | C241 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C241 | C3 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 246 |
| transitive degree | μt(G) = 1205 |
415 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3615, 3);