Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C131 ⋊ C2 |
| Sylow | C131 ⋊ #555 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D131 |
| commutator, socle | C22×C131 | C24 |
| Fitting | C4⋊Q8×C131 | C2 |
| hypercenter | C4⋊Q8 | D131 |
| hypocenter | C131 | #555 |
| LCS | G ▷ C22×C131 ▷ C131 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
236 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|b^2=f,c^2=e,d^2=e,b^a=be,c^a=cf,g^a=g^130,d^b=de,g^b=g^130,g^c=g^130935 conjugacy classes — view the full character table.
| maximal subgroup of | #30665042, #30665045, #30665104, … |
| maximal normal subgroup of | #30665042, #30665045, #30665104, … |
| maximal quotient of | #30668845, #30668912, #30668998, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 1265);