Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72×C19 · Schur multiplier (H2) = C3×C7 |
| direct product | C72×C3⋊D3×C19 |
| unambiguous semidirect product | C3⋊(D3×C72×C19) |
| Fitting, socle, Hall | C32×C72×C19 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C72×C19 |
| Hall | C32×C72 ⋊ C2×C19 |
| Hall | C32×C19 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72×C19 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C2×C72×C19 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C19 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C72×C19 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8379 |
5586 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×C19×#157, C72×C19⋊#157, C7×C19×C7⋊#157, … |
| maximal normal subgroup of | C72×C19×#157, C72×C19⋊#157, C7×C19×C7⋊#157, … |
| maximal quotient of | C72×C19×C3⋊Dic3, C2×C72×C3⋊D3×C19 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 407);