Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C7 |
| direct product | C19⋊C3×#64425 |
| Fitting, socle, derived, Hall | C72×C19 ⋊ C2×C32 |
| Hall | C19⋊C3×#3862 ⋊ C2 |
| Hall | C19×C7⋊D7 ⋊ C32 |
| Hall | C7⋊D7 ⋊ C3×C19⋊C3 |
| Sylow | C72 ⋊ C2×C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×#64425 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C19 | C2×C32 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 399 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | (C19⋊C3)⋊#10596885, C19⋊C3×#10596885, #45691989, … |
| maximal normal subgroup of | (C19⋊C3)⋊#10596885, C19⋊C3×#10596885, #45691989, … |
| maximal quotient of | C19⋊C3×#10596875, C2×C19⋊C3×#64425 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 183);