Finite Group DatabasebetaFinite Group Databasebeta| order | 17490 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C53 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D11×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C53 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C3×C5×C53 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C11×C53 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C3×C5×C53 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8745 |
5565 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D11×D53, C3×D5×D11×C53, C3×D11×D265, … |
| maximal normal subgroup of | C3×C5×D11×D53, C3×D5×D11×C53, C3×D11×D265, … |
| maximal quotient of | C3×C5×Dic11×C53, C2×C3×C5×D11×C53 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17490, 4);