Finite Group DatabasebetaFinite Group Databasebeta| order | 36390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×C1213⋊C3 |
| unambiguous semidirect product | (C2×C1213)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C5×C1213)⋊C3 |
| Fitting, socle, Hall | C2×C5×C1213 ⋊ C3 |
| derived, Sylow | C1213 ⋊ C2×C3×C5 |
| Hall | C5×C1213 ⋊ C2×C3 |
| Hall | C2×C1213 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C1213⋊C3 |
| commutator, cosocle, hypocenter | C1213 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C1213 | C3 |
| LCS | G ▷ C1213 | |
| UCS | C1 ◁ C2×C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12130 |
4070 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36390, 2);