Finite Group DatabasebetaFinite Group Databasebeta| order | 6736 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic421 |
| Sylow | C421 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D421 |
| commutator | C2×C421 | C2×C4 |
| Fitting | C2×C4×C421 | C2 |
| socle | C22×C421 | C22 |
| hypercenter | C2×C4 | D421 |
| hypocenter | C421 | C4⋊C4 |
| LCS | G ▷ C2×C421 ▷ C421 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,421|a^2=d,b^2=c,b^a=bc,e^a=e^4201690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27212287, #27212288, #27212290, … |
| maximal normal subgroup of | #27212287, #27212288, #27212290, … |
| maximal quotient of | #27212273, C4⋊#16809890, #27212298, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6736, 20);