Finite Group DatabasebetaFinite Group Databasebeta| order | 6736 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D421⋊C8 |
| derived, Sylow | C421 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #13132997 |
| commutator, hypocenter | C421 | C2×C8 |
| Frattini | C2 | C2×#13132997 |
| Fitting | C4×C421 | C4 |
| socle | C2×C421 | C2×C4 |
| LCS | G ▷ C421 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,421|a^2=c,c^2=d,e^a=e^29,e^b=e^420,e^c=e^420436 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#13132997, #27212420, #27212428, … |
| maximal normal subgroup of | C8×#13132997, #27212420, #27212428, … |
| maximal quotient of | C4×#16809897, #27212423, #27212433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6736, 48);