Finite Group DatabasebetaFinite Group Databasebeta| order | 10408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#19104543 |
| unambiguous semidirect product | D1301⋊C4 |
| Fitting, socle | C2×C1301 ⋊ C4 |
| derived, Sylow | C1301 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19104543 |
| commutator, hypocenter | C1301 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1301 | C4 |
| prime radical | C2×D1301 | C2 |
| cosocle | D1301 | C22 |
| LCS | G ▷ C1301 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
658 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#19104543, C22⋊#19104543, C4⋊#19104543, … |
| maximal normal subgroup of | C4×#19104543, C22⋊#19104543, C4⋊#19104543, … |
| maximal quotient of | C4×#19104543, C22⋊#19104543, C4⋊#19104543, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10408, 14);