Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C131 ⋊ #350 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C22⋊D131 |
| commutator | C4×C131 | C2×C8 |
| Frattini | C2×C8 | C2×D131 |
| Fitting | #131×C131 | C2 |
| socle | C2×C131 | C22⋊C8 |
| hypercenter | #131 | D131 |
| hypocenter | C131 | #350 |
| LCS | G ▷ C4×C131 ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #131 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^130,c^b=cf,d^b=df1328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #350×D131, C2×#22553096, #30667587, … |
| maximal normal subgroup of | #350×D131, C2×#22553096, #30667587, … |
| maximal quotient of | #30663887, #30663903, D4⋊(C131⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 333);