Finite Group DatabasebetaFinite Group Databasebeta| order | 5310 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C59 · Schur multiplier (H2) = C1 |
| direct product | C5×D9×C59 |
| unambiguous semidirect product | C9⋊(C2×C5×C59) |
| Fitting, Hall | C5×C9×C59 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C5×C59 |
| Hall | C9×C59 ⋊ C2×C5 |
| Hall | C5×C9 ⋊ C2×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C59 | D9 |
| commutator, hypocenter | C9 | C2×C5×C59 |
| Frattini | C3 | C5×D3×C59 |
| Fitting | C5×C9×C59 | C2 |
| socle | C3×C5×C59 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C5×C59 | |
24 conjugacy classes of subgroups.
1770 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C25×C59, C52×D9×C59, C5×C59×D45, … |
| maximal normal subgroup of | D9×C25×C59, C52×D9×C59, C5×C7×D9×C59 |
| maximal quotient of | D9×C25×C59, C52×D9×C59, C5×C59×D45, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5310, 5);