Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | #350×D67 |
| Fitting | #350×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#350 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D4×D67 |
| commutator | C4×C67 | C22×C8 |
| Frattini | C2×C8 | C22×D67 |
| Fitting | #350×C67 | C2 |
| socle | C2×C67 | C2×C22⋊C8 |
| hypercenter | #350 | D67 |
| hypocenter | C67 | C2×#350 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #350 | |
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
980 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#350×D67, #2117×D67, #31008535, … |
| maximal normal subgroup of | C2×#350×D67, #2117×D67, #31008535, … |
| maximal quotient of | #1315×D67, #30764904, #1323×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6132);