Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#11725075 |
| derived, Sylow | C72 ⋊ C2×C9×C19 |
| Hall | C19×#89205 ⋊ C2 |
| Hall | C7×D7×C19 ⋊ C9 |
| Hall | C72×C19 ⋊ C2×C9 |
| Hall | #89205 ⋊ C2×C19 |
| Hall | C7×D7 ⋊ C9×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C19 | #64422 |
| commutator, hypocenter | C72 | C2×C9×C19 |
| Frattini | C3 | C19×#64422 |
| Fitting, socle | C3×C72×C19 | C2×C3 |
| prime radical | C3×C7×D7×C19 | C3 |
| cosocle | C3×C72 | C2×C3×C19 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C19 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2394 |
969 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#11725075⋊C2, #11725075⋊D19, D19×#11725075, … |
| maximal normal subgroup of | C19×#11725075⋊C2, #11725075⋊D19, D19×#11725075, … |
| maximal quotient of | C19×#13183531, C2×C19×#11725075 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 114);