Finite Group DatabasebetaFinite Group Databasebeta| order | 8076 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic673⋊C3 |
| derived, Sylow | C673 ⋊ C3×C4 |
| Hall | Dic673 ⋊ C3 |
| Hall | C673⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D673⋊C3 |
| commutator, hypocenter | C673 | C3×C4 |
| Fitting, socle | C2×C673 | C2×C3 |
| LCS | G ▷ C673 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,673,2|a^2=d,c^a=c^672,c^b=c^255236 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic673⋊C3, C3⋊(Dic673⋊C3) |
| maximal normal subgroup of | C3×Dic673⋊C3 |
| maximal quotient of | Dic673⋊C9, C3×Dic673⋊C3, C3⋊(Dic673⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8076, 2);