Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C67 · Schur multiplier (H2) = C2 |
| direct product | C67×#1417 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C67 | D16 |
| commutator | C16 | C2×C4×C67 |
| Frattini, cosocle | C2×C16 | C22×C67 |
| socle | C2×C67 | #357 |
| prime radical | #508×C67 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C67 ◁ C2×C4×C67 ◁ C2×C8×C67 ◁ C2×C16×C67 ◁ G | |
72 conjugacy classes of subgroups.
2546 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 149);