Finite Group DatabasebetaFinite Group Databasebeta| order | 5610 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C17 · Schur multiplier (H2) = C1 |
| direct product | C11×C17×D15 |
| unambiguous semidirect product | C3⋊(D5×C11×C17) |
| unambiguous semidirect product | C5⋊(D3×C11×C17) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C17 | D15 |
| commutator, hypocenter | C3×C5 | C2×C11×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C11×C17 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C11×C17 | |
32 conjugacy classes of subgroups.
1683 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D15×D17, C17×D11×D15, D15×D187, … |
| maximal normal subgroup of | C11×D15×D17, C17×D11×D15, D15×D187, … |
| maximal quotient of | C11×C17×Dic15, C2×C11×C17×D15, C11×C17×D45, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5610, 14);