Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C131 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D131 |
| commutator, socle | C2×C131 | C22×C8 |
| Fitting | #131×C131 | C2 |
| hypercenter | #131 | D131 |
| hypocenter | C131 | #504 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C8 ◁ #131 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=d,d^2=e,e^2=f,g^a=g^130,c^b=cf1340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30667795, #30667798, #30667800, … |
| maximal normal subgroup of | #30667795, #30667798, #30667800, … |
| maximal quotient of | #30667558, #30667575, #30667720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 966);