Finite Group DatabasebetaFinite Group Databasebeta| order | 11730 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C5×C17×D69 |
| unambiguous semidirect product | C3⋊(C5×C17×D23) |
| unambiguous semidirect product | C23⋊(C5×D3×C17) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C17 | D69 |
| commutator, cosocle, hypocenter | C3×C23 | C2×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C17×C23 | C2 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C5×C17 | |
32 conjugacy classes of subgroups.
3060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×C17×D23, C5×D17×D69, C5×D51⋊D23, … |
| maximal normal subgroup of | C5×D3×C17×D23, C5×D17×D69, C5×D51⋊D23, … |
| maximal quotient of | C5×C17×Dic69, C2×C5×C17×D69, C5×C17×D207, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11730, 10);