Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#16863509 |
| Fitting | C2×#97×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#442 |
608 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30751255, #30751257, #30751283, … |
| maximal normal subgroup of | #30751255, #30751257, #30751283, … |
| maximal quotient of | C2×#22559034, C2×#22559075, C2×#22559124, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13304);