Finite Group DatabasebetaFinite Group Databasebeta| order | 4298 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D307 |
| unambiguous semidirect product | C307⋊(C2×C7) |
| Fitting, socle, Hall | C7×C307 ⋊ C2 |
| derived, Sylow | C307 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D307 |
| commutator, cosocle, hypocenter | C307 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C307 | C2 |
| LCS | G ▷ C307 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 314 |
| transitive degree | μt(G) = 2149 |
1085 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×D307, C7×D921, C7×D307⋊C3, … |
| maximal normal subgroup of | C3×C7×D307, C7×D307⋊C3, ΓL(1,𝔽8)×D307, … |
| maximal quotient of | C3×C7×D307, C7×D921, C5×C7×D307, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4298, 2);