Finite Group DatabasebetaFinite Group Databasebeta| order | 18207 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C289 · Schur multiplier (H2) = C1 |
| direct product | C7⋊C9×C289 |
| unambiguous semidirect product | C7⋊(C9×C289) |
| unambiguous semidirect product | (C7×C289)⋊C9 |
| derived, Sylow | C7 ⋊ C9×C289 |
| Hall | C7×C289 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C289 | ΓL(1,𝔽8) |
| commutator, hypocenter | C7 | C9×C289 |
| Frattini | C3×C17 | C17×ΓL(1,𝔽8) |
| Fitting | C3×C7×C289 | C3 |
| socle, prime radical, cosocle | C3×C7×C17 | C3×C17 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C3×C289 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18207 |
4335 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7⋊C9×D289, D7⋊C9×C289, (C7⋊C9)⋊D289, … |
| maximal normal subgroup of | C7⋊C9×D289, D7⋊C9×C289, (C7⋊C9)⋊D289, … |
| maximal quotient of | C2×C7⋊C9×C289 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18207, 2);