Finite Group DatabasebetaFinite Group Databasebeta| order | 36780 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#14578580⋊C3 |
| unambiguous semidirect product | #14578580⋊(C3×C5) |
| unambiguous semidirect product | (C5×#14578580)⋊C3 |
| Fitting, socle, Hall | C5×C613 ⋊ C3×C4 |
| derived, Sylow | C613 ⋊ C3×C4×C5 |
| Hall | C5×#14578580 ⋊ C3 |
| Hall | C5×C613⋊C3 ⋊ C4 |
| Hall | #14578580 ⋊ C3×C5 |
| Hall | C613⋊C3 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #14578580⋊C3 |
| commutator, hypocenter | C613 | C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C613 | C3×C4 |
| prime radical | C5×D613⋊C3 | C2 |
| cosocle | D613 | C2×C3×C5 |
| LCS | G ▷ C613 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3065 |
315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36780, 14);