Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×Dic263 |
| derived, Sylow | C263 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D263 |
| commutator, hypocenter | C263 | C4×C8 |
| Frattini | C2×C4 | C2×D263 |
| Fitting | C2×C8×C263 | C2 |
| socle | C22×C263 | C2×C4 |
| LCS | G ▷ C263 | |
| UCS | C1 ◁ C2×C8 | |
44 conjugacy classes of subgroups.
2128 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×Dic263, #30681713, Dic263⋊C16, … |
| maximal normal subgroup of | C16×Dic263, #30681713, Dic263⋊C16, … |
| maximal quotient of | C8×C263⋊C8, #30681660, #30681692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 54);