Finite Group DatabasebetaFinite Group Databasebeta| order | 6416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#15692006 |
| derived, Sylow | C401 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #13107944 |
| commutator, hypocenter | C401 | C2×C8 |
| Frattini | C2 | C2×#13107944 |
| Fitting, socle | C22×C401 | C4 |
| LCS | G ▷ C401 | |
| UCS | C1 ◁ C22 | |
22 conjugacy classes of subgroups.
416 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#15692006, #27165792, C22⋊#15692006, … |
| maximal normal subgroup of | C4×#15692006, #27165792, C22⋊#15692006, … |
| maximal quotient of | C4×#15692006, C22⋊#15692006, C4⋊#15692006, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6416, 47);