Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×C263⋊C16 |
| unambiguous semidirect product | (C2×C263)⋊C16 |
| derived, Sylow | C263 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D263 |
| commutator, hypocenter | C263 | C2×C16 |
| Frattini | C8 | C2×D263 |
| Fitting | C2×C8×C263 | C2 |
| socle | C22×C263 | C8 |
| LCS | G ▷ C263 | |
| UCS | C1 ◁ C2×C8 | |
28 conjugacy classes of subgroups.
2128 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×Dic263, C4×C263⋊C16, #30681713, … |
| maximal normal subgroup of | C16×Dic263, C4×C263⋊C16, #30681713, … |
| maximal quotient of | C4×C263⋊C16, C22⋊(C263⋊C16), C4⋊(C263⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 84);