Finite Group DatabasebetaFinite Group Databasebeta| order | 8408 |
| automorphism | Aut(G) order 8828400 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4204 |
| unambiguous semidirect product | C4⋊D1051 |
| Fitting | C4×C1051 ⋊ C2 |
| Sylow | C1051 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1051 |
| commutator, socle | C2×C1051 | C22 |
| Fitting | C4×C1051 | C2 |
| hypercenter | C4 | D1051 |
| hypocenter | C1051 | D4 |
| LCS | G ▷ C2×C1051 ▷ C1051 | |
| UCS | C1 ◁ C2 ◁ C4 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1051|b^a=bc,d^a=d^1050,d^b=d^10502105 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30681218, D8408, #30681220, … |
| maximal normal subgroup of | #30681218, D8408, #30681220, … |
| maximal quotient of | (C2×D1051)⋊C4, C4⋊Dic1051, D8408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8408, 10);