Finite Group DatabasebetaFinite Group Databasebeta| order | 16646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | D41×C29⋊C7 |
| unambiguous semidirect product | C41⋊(C2×C29⋊C7) |
| unambiguous semidirect product | (C29×D41)⋊C7 |
| Fitting, socle, derived, Hall | C29×C41 ⋊ C2×C7 |
| Hall | C41×C29⋊C7 ⋊ C2 |
| Hall | C29×D41 ⋊ C7 |
| Sylow | C41 ⋊ C2×C29⋊C7 |
| Sylow | C29 ⋊ C7×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C41 | C2×C7 |
| LCS | G ▷ C29×C41 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1189 |
242 conjugacy classes — view the full character table.
| maximal subgroup of | #18011703⋊C7, D41×D29⋊C7, #4223×C29⋊C7, … |
| maximal normal subgroup of | #18011703⋊C7, D41×D29⋊C7, #4223×C29⋊C7, … |
| maximal quotient of | Dic41×C29⋊C7, C2×D41×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16646, 10);