Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| isoclinism | isoclinic class of D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×Dic45 |
| unambiguous semidirect product | C9⋊(Dic5×C37) |
| derived, Hall | C5×C9 ⋊ C4×C37 |
| Hall | C5×C9×C37 ⋊ C4 |
| Hall | C9×C37 ⋊ Dic5 |
| Hall | C5×C37 ⋊ Dic9 |
| Sylow | C9 ⋊ Dic5×C37 |
| Sylow | C5 ⋊ Dic9×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | D45 |
| commutator, hypocenter | C5×C9 | C4×C37 |
| Frattini | C2×C3 | D15×C37 |
| Fitting | C2×C5×C9×C37 | C2 |
| socle | C2×C3×C5×C37 | D3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C2×C37 | |
36 conjugacy classes of subgroups.
1776 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×Dic225, C5×C37×Dic45, C37×C9⋊#1039, … |
| maximal normal subgroup of | C5×C37×Dic45 |
| maximal quotient of | C37×Dic225, C5×C37×Dic45, C37×C9⋊#1039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 11);