Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#14523970 |
| Sylow | C67 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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 | C8×#14523970, #30746542, #30746544, … |
| maximal normal subgroup of | C8×#14523970, #30746542, #30746544, … |
| maximal quotient of | C4×D4⋊(C67⋊C8), C4×Q8⋊(C67⋊C8), #30746443, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4315);