Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C7⋊C9×D133 |
| derived, Hall | C72×C19 ⋊ C2×C9 |
| Hall | C7×C19×C7⋊C9 ⋊ C2 |
| Hall | C7×D133 ⋊ C9 |
| Hall | C7×C7⋊C9 ⋊ D19 |
| Sylow | C72 ⋊ C9×D19 |
| Sylow | C19 ⋊ D7×C7⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×D133 |
| commutator, hypocenter | C72×C19 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C19 | C2×C3 |
| prime radical | C3×C7×D133 | C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2394 |
1020 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7⋊C9×D133, ((C7⋊C9)⋊D7)⋊D19, D7×D19×C7⋊C9, … |
| maximal normal subgroup of | D7⋊C9×D133, ((C7⋊C9)⋊D7)⋊D19, D7×D19×C7⋊C9, … |
| maximal quotient of | C7⋊C9×Dic133, C2×C7⋊C9×D133 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 136);