Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| isoclinism | isoclinic class of #4296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72×C9 · Schur multiplier (H2) = C7 |
| direct product | C2×C72×#4296 |
| Fitting, socle, Hall | C2×C72×C19 ⋊ C9 |
| derived, Sylow | C19 ⋊ C2×C72×C9 |
| Hall | C72×C19 ⋊ C2×C9 |
| Hall | C2×C19 ⋊ C72×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | #4296 |
| commutator, hypocenter | C19 | C2×C72×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C19 | C9 |
| prime radical | C2×C72×C19⋊C3 | C3 |
| cosocle | C19⋊C3 | C2×C3×C72 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C72 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1862 |
1078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×#4296⋊C4, C7×#4296⋊Dic7, C7×Dic7×#4296, … |
| maximal normal subgroup of | C72×#4296⋊C4, C7×#4296⋊Dic7, C7×Dic7×#4296, … |
| maximal quotient of | C4×C72×#4296, C22×C72×#4296 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 259);