Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×#11761613 |
| Fitting | C2×C4×D4×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×C4×D8 |
616 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30750403, #30750404, #30750406, … |
| maximal normal subgroup of | #30750403, #30750404, #30750406, … |
| maximal quotient of | C2×C8×#11761613, C2×#22559036, C2×#22559038, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13259);