Finite Group DatabasebetaFinite Group Databasebeta| order | 16762 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C17 |
| direct product | C29×C17⋊D17 |
| unambiguous semidirect product | C17⋊(C29×D17) |
| Fitting, socle, Hall | C172×C29 ⋊ C2 |
| derived, Sylow | C172 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | C17⋊D17 |
| commutator, cosocle, hypocenter | C172 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C172×C29 | C2 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C29 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8381 |
4234 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C29×D172, (C17⋊D17)⋊D29, D29×C17⋊D17, … |
| maximal normal subgroup of | C29×D172, (C17⋊D17)⋊D29, D29×C17⋊D17, … |
| maximal quotient of | C29×#11923880, C2×C29×C17⋊D17 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16762, 7);