Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| isoclinism | isoclinic class of D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×C9×Dic41 |
| derived, Sylow | C41 ⋊ C4×C5×C9 |
| Hall | C5×C9×C41 ⋊ C4 |
| Hall | C9×C41 ⋊ C4×C5 |
| Hall | C5×C41 ⋊ C4×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C9 | D41 |
| commutator, hypocenter | C41 | C4×C5×C9 |
| Frattini | C2×C3 | C3×C5×D41 |
| Fitting | C2×C5×C9×C41 | C2 |
| socle | C2×C3×C5×C41 | C2×C3 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2×C5×C9 | |
36 conjugacy classes of subgroups.
1980 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×Dic41⋊C25, C9×C25×Dic41, C5×C9×Dic41⋊C5, … |
| maximal normal subgroup of | C9×Dic41⋊C25, C9×C25×Dic41, C5×C9×Dic41⋊C5, … |
| maximal quotient of | C9×C25×Dic41, C52×C9×Dic41, C5×C9×Dic205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 6);