Finite Group DatabasebetaFinite Group Databasebeta| order | 804 |
| isoclinism | isoclinic class of D67⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C67⋊C3)⋊C4 |
| unambiguous semidirect product | Dic67⋊C3 |
| derived, Sylow | C67 ⋊ C3×C4 |
| Hall | Dic67 ⋊ C3 |
| Hall | C67⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D67⋊C3 |
| commutator, hypocenter | C67 | C3×C4 |
| Fitting, socle, cosocle | C2×C67 | C2×C3 |
| prime radical | C2×C67⋊C3 | C2 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 268 |
Polycyclic presentation:
2,3,2,67|a^2=c,d^a=d^66,d^b=d^3734 conjugacy classes — view the full character table.
| maximal subgroup of | (C67⋊C3)⋊Q8, C4×D67⋊C3, C2×(C67⋊C3)⋊C4, … |
| maximal normal subgroup of | (C67⋊C3)⋊Q8, C4×D67⋊C3, C2×(C67⋊C3)⋊C4, … |
| maximal quotient of | (C67⋊C3)⋊C8, C2×(C67⋊C3)⋊C4, Dic67⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(804, 1);