Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C263⋊C8) |
| Sylow | C263 ⋊ C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×D263 |
| commutator | C2×C263 | C2×C8 |
| Fitting | C42×C263 | C2 |
| socle | C22×C263 | C2×C4 |
| hypercenter | C42 | D263 |
| hypocenter | C263 | C4⋊C8 |
| LCS | G ▷ C2×C263 ▷ C263 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,263|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^2622116 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊(C263⋊C8), #30681667, Q8⋊(C263⋊C8), … |
| maximal normal subgroup of | D4⋊(C263⋊C8), #30681667, Q8⋊(C263⋊C8), … |
| maximal quotient of | #30681689, #30681691, #30681693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 76);