Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C72×C19 ⋊ C2×C9 |
| Hall | C7×#11924776 ⋊ C2 |
| Hall | C19×C7⋊D7 ⋊ C9 |
| Hall | C7⋊D7 ⋊ #4294 |
| Sylow | C72 ⋊ C2×#4294 |
| Sylow | C19 ⋊ (C7⋊C9)⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #19150308 |
| commutator, hypocenter | C72×C19 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C19 | C2×C3 |
| prime radical | C3×C19×C7⋊D7 | C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1197 |
Polycyclic presentation:
2,3,7^2,19,3|b^3=f,c^a=c^6,d^a=d^6,c^b=c^2,e^b=e^7534 conjugacy classes — view the full character table.
| maximal subgroup of | #14558786⋊D7, D7×#14558784, #14558780⋊D7, … |
| maximal normal subgroup of | #14558786⋊D7, D7×#14558784, #14558780⋊D7, … |
| maximal quotient of | #45691500, C2×#30660596 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 123);