Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×#16863159 |
| Sylow | C67 ⋊ C2×#340 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D268 |
| commutator | C4×C67 | C2×C42 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | C23×C8×C67 | C2 |
| socle | C24×C67 | D4 |
| hypercenter | C23×C8 | D67 |
| hypocenter | C67 | C2×#340 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
512 conjugacy classes of subgroups.
2168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30742974, #30742976, #30742992, … |
| maximal normal subgroup of | #30742974, #30742976, #30742992, … |
| maximal quotient of | C2×#22558044, #30745297, #30745307, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4224);