Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic615 |
| unambiguous semidirect product | C3⋊(C3×Dic205) |
| derived | C3×C5×C41 ⋊ C3×C4 |
| Hall | C32×C5×C41 ⋊ C4 |
| Hall | C32×C41 ⋊ Dic5 |
| Hall | C5×C41 ⋊ C3×Dic3 |
| Hall | C32×C5 ⋊ Dic41 |
| Sylow | C41 ⋊ C3×Dic15 |
| Sylow | C32 ⋊ Dic205 |
| Sylow | C5 ⋊ C3×Dic123 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D615 |
| commutator, hypocenter | C3×C5×C41 | C3×C4 |
| Frattini | C2 | C3×D615 |
| Fitting, socle | C2×C32×C5×C41 | C2 |
| LCS | G ▷ C3×C5×C41 | |
| UCS | C1 ◁ C2×C3 | |
56 conjugacy classes of subgroups.
1854 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic3075, C3×C3⋊(Dic205⋊C5), C3×C3⋊#16861497, … |
| maximal normal subgroup of | C3×C3⋊(Dic205⋊C5), C3×C5×Dic615 |
| maximal quotient of | C3×Dic3075, C3×C3⋊#16861497, C3×C5×Dic615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 62);