Finite Group DatabasebetaFinite Group Databasebeta| order | 804 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D67 |
| Fitting, socle | C2×C3×C67 ⋊ C2 |
| derived, Sylow | C67 ⋊ C22×C3 |
| Hall | C3×C67 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D67 |
| commutator, cosocle, hypocenter | C67 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C67 | C2 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C3 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 402 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×D67, #13107967, #13107968, … |
| maximal normal subgroup of | Dic3×D67, #13107967, #13107968, … |
| maximal quotient of | C3×Dic134, C3×C4×D67, C3×D268, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(804, 12);