Finite Group DatabasebetaFinite Group Databasebeta| order | 6416 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q8×C401 ⋊ C2 |
| Sylow | C401 ⋊ SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D401 |
| commutator | C4×C401 | C22 |
| Frattini | C4 | C2×D401 |
| Fitting | Q8×C401 | C2 |
| socle | C2×C401 | D4 |
| hypercenter | Q8 | D401 |
| hypocenter | C401 | SD16 |
| LCS | G ▷ C4×C401 ▷ C2×C401 ▷ C401 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q8 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,401|a^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^4001007 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×D401, C2×#20264353, #27165757, … |
| maximal normal subgroup of | SD16×D401, C2×#20264353, #27165757, … |
| maximal quotient of | #27165657, #27165661, #27165668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6416, 27);