Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16862162 |
| Fitting | C2×M16×C131 ⋊ C2 |
| Sylow | C131 ⋊ C2×#100 |
186 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1322 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30665752, C4×#16862162, #30665880, … |
| maximal normal subgroup of | #30665752, C4×#16862162, #30665880, … |
| maximal quotient of | C2×#22553035, #30664281, #30664287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 525);