Finite Group DatabasebetaFinite Group Databasebeta| order | 18207 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C172 · Schur multiplier (H2) = C17 |
| direct product | C172×C7⋊C9 |
| unambiguous semidirect product | C7⋊(C9×C172) |
| unambiguous semidirect product | (C7×C17)⋊(C9×C17) |
| derived, Sylow | C7 ⋊ C9×C172 |
| Hall | C7×C172 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C172 | ΓL(1,𝔽8) |
| commutator, hypocenter | C7 | C9×C172 |
| Frattini | C3 | C172×ΓL(1,𝔽8) |
| Fitting, socle, prime radical | C3×C7×C172 | C3 |
| cosocle | C3×C7 | C3×C172 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C3×C172 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18207 |
4335 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C172×D7⋊C9, C17×C17⋊(D7⋊C9), C17⋊(C17⋊(D7⋊C9)), … |
| maximal normal subgroup of | C172×D7⋊C9, C17×C17⋊(D7⋊C9), C17⋊(C17⋊(D7⋊C9)), … |
| maximal quotient of | C2×C172×C7⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18207, 7);