Finite Group DatabasebetaFinite Group Databasebeta| order | 6416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C401 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #13107944 |
| commutator, hypocenter | C401 | C2×C8 |
| Frattini | C2 | C2×#13107944 |
| Fitting | C4×C401 | C4 |
| socle | C2×C401 | C2×C4 |
| LCS | G ▷ C401 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,401|a^2=c,c^2=d,e^a=e^20,e^b=e^400,e^c=e^400416 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#13107944, #27165791, #27165799, … |
| maximal normal subgroup of | C8×#13107944, #27165791, #27165799, … |
| maximal quotient of | C4×#15692006, #27165794, #27165804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6416, 48);