Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | M32×D131 |
| Fitting | M32×C131 ⋊ C2 |
| Sylow | C131 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D131 |
| commutator, socle | C2×C131 | C22×C8 |
| Fitting | M32×C131 | C2 |
| hypercenter | M32 | D131 |
| hypocenter | C131 | C2×M32 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C8 ◁ M32 | |
90 conjugacy classes of subgroups.
1340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #347×D131, #30667564, #349×D131, … |
| maximal normal subgroup of | #347×D131, #30667564, #349×D131, … |
| maximal quotient of | #346×D131, M32×Dic131, #30667554, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 962);