Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊Q8×C131 ⋊ C2 |
| Sylow | C131 ⋊ #461 |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=f,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,e^c=ef,g^c=g^130929 conjugacy classes — view the full character table.
| maximal subgroup of | #30665137, #30665139, #30665158, … |
| maximal normal subgroup of | #30665137, #30665139, #30665158, … |
| maximal quotient of | #30665333, #30665347, #30665357, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 751);