Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | B(4,𝔽2)×D67 |
| Fitting | B(4,𝔽2)×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×B(4,𝔽2) |
1018 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 1018 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.
560 conjugacy classes — view the full character table.
| maximal subgroup of | #2196×D67, #2197×D67, #2199×D67, … |
| maximal normal subgroup of | #2196×D67, #2197×D67, #2199×D67, … |
| maximal quotient of | #1595×D67, #1601×D67, #1596×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13892);