Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#16864213 |
| Fitting | C2×#131×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#578 |
1408 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 549 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 | #30771521, #30771524, #30771531, … |
| maximal normal subgroup of | #30771521, #30771524, #30771531, … |
| maximal quotient of | C2×#22568743, C2×#22568809, C2×#22569054, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 19277);