Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D7×#11924777 |
| derived, Hall | C72×C19 ⋊ C2×C9 |
| Hall | C7×#11924777 ⋊ C2 |
| Hall | C7×D7×C19 ⋊ C9 |
| Hall | C7×D7 ⋊ #4294 |
| Sylow | C72 ⋊ C2×#4294 |
| Sylow | C19 ⋊ D7×C7⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D7×#87705 |
| commutator, hypocenter | C72×C19 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C19 | C2×C3 |
| prime radical | C3×C7×D7×C19 | C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2394 |
705 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×#14558787, D7×#14558785, D7×#14558781, … |
| maximal normal subgroup of | D7×#14558787, D7×#14558785, D7×#14558781, … |
| maximal quotient of | Dic7×#11924777, C2×D7×#11924777 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 135);