Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| isoclinism | isoclinic class of D131 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C32×D131 |
| Fitting | C32×C131 ⋊ C2 |
| derived, Sylow | C131 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D131 |
| commutator, hypocenter | C131 | C2×C32 |
| Frattini | C16 | C2×D131 |
| Fitting | C32×C131 | C2 |
| socle | C2×C131 | C2×C16 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C32 | |
34 conjugacy classes of subgroups.
2144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×D131, #30664171, C2×C32×D131, … |
| maximal normal subgroup of | C64×D131, #30664171, C2×C32×D131, … |
| maximal quotient of | C32×Dic131, (C2×D131)⋊C32, Dic131⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 380);