Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#14524075 |
| Fitting | C22×Q16×C67 ⋊ C2 |
| Sylow | C67 ⋊ C22×#137 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D67 |
| commutator | C4×C67 | C25 |
| Frattini | C4 | C24×D67 |
| Fitting | C22×Q16×C67 | C2 |
| socle | C23×C67 | C2×D4 |
| hypercenter | C22×Q16 | D67 |
| hypocenter | C67 | C22×#137 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×Q16 | |
1464 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 525 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
968 conjugacy classes — view the full character table.
| maximal subgroup of | #30857195, #30857206, #30857231, … |
| maximal normal subgroup of | #30857195, #30857206, #30857231, … |
| maximal quotient of | C22×#16863403, C22×#16863396, C22×#16863437, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 19250);