Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#11725071 |
| derived, Hall | #89205 ⋊ C2×C19 |
| Hall | C19×#89205 ⋊ C2 |
| Hall | C72×C19 ⋊ D9 |
| Sylow | C72 ⋊ D9×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #11725071 |
| commutator, cosocle, hypocenter | #89205 | C2×C19 |
| Frattini | C3 | C19×#64418 |
| Fitting, socle | C3×C72×C19 | D3 |
| LCS | G ▷ #89205 | |
| UCS | C1 ◁ C19 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1197 |
741 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#11725071⋊C2, #11725071⋊D19, D19×#11725071, … |
| maximal normal subgroup of | C19×#11725071⋊C2, #11725071⋊D19, D19×#11725071, … |
| maximal quotient of | C19×#13183527, C2×C19×#11725071 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 139);