Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #332×D67 |
| Fitting | #332×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#332 |
256 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
665 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#332×D67, #1540×D67, #1542×D67, … |
| maximal normal subgroup of | C2×#332×D67, #1540×D67, #1542×D67, … |
| maximal quotient of | #1271×D67, #30743807, #30744109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 3152);