Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×D399 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)×D133) |
| Fitting, socle, derived | C3×C72×C19 ⋊ C2×C3 |
| Hall | C3×C7×C19×ΓL(1,𝔽8) ⋊ C2 |
| Hall | C72×C19 ⋊ C3×D3 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ D19 |
| Sylow | C72 ⋊ C3×D57 |
| Sylow | C19 ⋊ ΓL(1,𝔽8)×D21 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C19 | C2×C3 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2394 |
1005 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 388);