Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C7 |
| direct product | C7⋊D7×#4296 |
| Fitting, socle, derived, Hall | C72×C19 ⋊ C2×C9 |
| Hall | C72×#4296 ⋊ C2 |
| Hall | C19×C7⋊D7 ⋊ C9 |
| Sylow | C72 ⋊ C2×#4296 |
| Sylow | C19 ⋊ C9×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C19 | C2×C9 |
| prime radical | C19⋊C3×C7⋊D7 | C3 |
| cosocle | C72×C19⋊C3 | C2×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 931 |
286 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #4296⋊#5997, #4296×#5997, (#4296⋊D7)⋊D7, … |
| maximal normal subgroup of | #4296⋊#5997, #4296×#5997, (#4296⋊D7)⋊D7, … |
| maximal quotient of | #4296×C7⋊Dic7, C2×C7⋊D7×#4296 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 250);