Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C263⋊C32 |
| derived, Sylow | C263 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D263 |
| commutator, hypocenter | C263 | C32 |
| Fitting | C16×C263 | C2 |
| socle | C2×C263 | C16 |
| LCS | G ▷ C263 | |
| UCS | C1 ◁ C16 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,263|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^2622128 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D263, C2×C263⋊C32, #30681771, … |
| maximal normal subgroup of | C32×D263, C2×C263⋊C32, #30681771, … |
| maximal quotient of | C263⋊C64, C2×C263⋊C32 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 52);