Finite Group DatabasebetaFinite Group Databasebeta| order | 4326 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D721 |
| Fitting, socle, Hall | C3×C7×C103 ⋊ C2 |
| derived, Hall | C7×C103 ⋊ C2×C3 |
| Hall | C3×C103 ⋊ D7 |
| Sylow | C103 ⋊ C3×D7 |
| Hall | C3×C7 ⋊ D103 |
| Sylow | C7 ⋊ C3×D103 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D721 |
| commutator, cosocle, hypocenter | C7×C103 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C103 | C2 |
| LCS | G ▷ C7×C103 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 2163 |
1086 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D721, (C103⋊C9)⋊D7, (C7⋊C9)⋊D103, … |
| maximal normal subgroup of | C9×D721, (C103⋊C9)⋊D7, (C7⋊C9)⋊D103, … |
| maximal quotient of | C9×D721, C3×D2163, C32×D721, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4326, 8);