Finite Group DatabasebetaFinite Group Databasebeta| order | 4326 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D103⋊C3 |
| unambiguous semidirect product | D103⋊(C3×C7) |
| unambiguous semidirect product | (C103⋊C3)⋊(C2×C7) |
| Fitting, socle, Hall | C7×C103 ⋊ C2×C3 |
| derived, Sylow | C103 ⋊ C2×C3×C7 |
| Hall | C7×C103⋊C3 ⋊ C2 |
| Hall | C7×D103 ⋊ C3 |
| Hall | C103⋊C3 ⋊ C2×C7 |
| Hall | D103 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D103⋊C3 |
| commutator, cosocle, hypocenter | C103 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C103 | C2×C3 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 110 |
| transitive degree | μt(G) = 721 |
161 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4326, 13);