Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#16863317 |
| Sylow | C67 ⋊ C2×#395 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D67 |
| commutator | C23×C67 | C24 |
| Frattini | C23 | C23×D67 |
| Fitting | C2×#95×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C2×#95 | D67 |
| hypocenter | C67 | C2×#395 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
908 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30750824, #30750829, #30756047, … |
| maximal normal subgroup of | #30750824, #30750829, #30756047, … |
| maximal quotient of | C2×#22558461, C2×#22558463, C2×#22558473, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 7721);