Finite Group DatabasebetaFinite Group Databasebeta| order | 4046 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C17 |
| direct product | C7×C17⋊D17 |
| unambiguous semidirect product | C17⋊(C7×D17) |
| Fitting, socle, Hall | C7×C172 ⋊ C2 |
| derived, Sylow | C172 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C17⋊D17 |
| commutator, cosocle, hypocenter | C172 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C172 | C2 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C7 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2023 |
1022 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4046, 7);