Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C8×(C2×D67)⋊C4 |
| Fitting | C2×C4×C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C8×C22⋊C4 |
384 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30770909, C16×(C2×D67)⋊C4, #30770914, … |
| maximal normal subgroup of | #30770909, C16×(C2×D67)⋊C4, #30770914, … |
| maximal quotient of | C8×(C2×D67)⋊C8, #30746305, #30746321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4282);