Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16862222 |
| Fitting | C22×Q8×C131 ⋊ C2 |
| Sylow | C131 ⋊ C2×C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D131 |
| commutator | C22×C131 | C24 |
| Frattini | C22 | C23×D131 |
| Fitting | C22×Q8×C131 | C2 |
| socle | C23×C131 | C23 |
| hypercenter | C22×Q8 | D131 |
| hypocenter | C131 | C2×C22⋊Q8 |
| LCS | G ▷ C22×C131 ▷ C131 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30666265, #30666270, #30666381, … |
| maximal normal subgroup of | #30666265, #30666270, #30666381, … |
| maximal quotient of | C2×#22553169, C2×#22553183, C2×#22553193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 1044);