Finite Group DatabasebetaFinite Group Databasebeta| order | 6736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C421 ⋊ C2 |
| Sylow | C421 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D421 |
| commutator, socle | C2×C421 | C23 |
| Fitting | Q8×C421 | C2 |
| hypercenter | Q8 | D421 |
| hypocenter | C421 | #41 |
| LCS | G ▷ C2×C421 ▷ C421 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,421|c^2=d,b^a=bd,e^a=e^420,e^b=e^420,e^c=e^4201060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27212387, #27212389, #27212393, … |
| maximal normal subgroup of | #27212387, #27212389, #27212393, … |
| maximal quotient of | #27212324, #27212328, Q8×Dic421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6736, 41);