Finite Group DatabasebetaFinite Group Databasebeta| order | 14427 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C7×C229 ⋊ C32 |
| Sylow | C229 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C229⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C229 | C32 |
| LCS | G ▷ C7×C229 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1603 |
395 conjugacy classes. The character table is too large to display.
| maximal subgroup of | ΓL(1,𝔽8)⋊(D229⋊C3), AGL(1,𝔽7)×C229⋊C3, ΓL(1,𝔽8)×D229⋊C3, … |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊(D229⋊C3), AGL(1,𝔽7)×C229⋊C3, ΓL(1,𝔽8)×D229⋊C3, … |
| maximal quotient of | C2×ΓL(1,𝔽8)×C229⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14427, 7);