Finite Group DatabasebetaFinite Group Databasebeta| order | 14630 |
| isoclinism | isoclinic class of D209 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×D209 |
| unambiguous semidirect product | C19⋊(C5×C7×D11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | D209 |
| commutator, cosocle, hypocenter | C11×C19 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C11×C19 | C2 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C5×C7 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7315 |
3710 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×D11×D19, C5×D7×D209, C5×D77⋊D19, … |
| maximal normal subgroup of | C5×C7×D11×D19, C5×D7×D209, C5×D77⋊D19, … |
| maximal quotient of | C5×C7×Dic209, C2×C5×C7×D209 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14630, 5);