Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C41 · Schur multiplier (H2) = C1 |
| direct product | C9×Dic5×C41 |
| derived, Sylow | C5 ⋊ C4×C9×C41 |
| Hall | C5×C9×C41 ⋊ C4 |
| Hall | C5×C41 ⋊ C4×C9 |
| Hall | C5×C9 ⋊ C4×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9×C41 | D5 |
| commutator, hypocenter | C5 | C4×C9×C41 |
| Frattini | C2×C3 | C3×D5×C41 |
| Fitting | C2×C5×C9×C41 | C2 |
| socle | C2×C3×C5×C41 | C2×C3 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C9×C41 | |
36 conjugacy classes of subgroups.
2952 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C41×Dic25, C9×Dic5×C41⋊C5, C5×C9×Dic5×C41, … |
| maximal normal subgroup of | C9×Dic5×C41⋊C5, C5×C9×Dic5×C41 |
| maximal quotient of | C9×C41×Dic25, C5×C9×Dic5×C41, C9×C41×#1039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 7);