Finite Group DatabasebetaFinite Group Databasebeta| order | 6416 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C401 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #15692008 |
| commutator, hypocenter | C401 | C16 |
| Fitting, socle | C2×C401 | C8 |
| LCS | G ▷ C401 | |
| UCS | C1 ◁ C2 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,401|a^2=b,b^2=c,c^2=d,e^a=e^45,e^b=e^20,e^c=e^400116 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20264378, #27165832, #27165833, … |
| maximal normal subgroup of | C2×#20264378, #27165832, #27165833, … |
| maximal quotient of | #27165827, C2×#20264378 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6416, 52);