Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16863654 |
| Sylow | C67 ⋊ C2×#470 |
492 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#22558196, C2×#22558198, C2×#22558202, … |
| maximal normal subgroup of | C2×#22558196, C2×#22558198, C2×#22558202, … |
| maximal quotient of | C2×#22559698, C2×#22559732, C2×#22559784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14112);