Finite Group DatabasebetaFinite Group Databasebeta| order | 17690 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C61 · Schur multiplier (H2) = C1 |
| direct product | C5×D29×C61 |
| unambiguous semidirect product | C29⋊(C2×C5×C61) |
| Fitting, socle, Hall | C5×C29×C61 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C5×C61 |
| Hall | C29×C61 ⋊ C2×C5 |
| Hall | C5×C29 ⋊ C2×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C61 | D29 |
| commutator, cosocle, hypocenter | C29 | C2×C5×C61 |
| Frattini | C1 | G |
| Fitting, socle | C5×C29×C61 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C5×C61 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8845 |
4880 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C61×#1181, C5×#20296687, C5×D29×D61, … |
| maximal normal subgroup of | C5×C61×#1181, C5×#20296687, C5×D29×D61, … |
| maximal quotient of | C5×C61×Dic29, C2×C5×D29×C61 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17690, 4);