Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #532×C67 ⋊ C2 |
| Sylow | C67 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D67 |
| commutator, socle | C22×C67 | C25 |
| Frattini | C22 | C24×D67 |
| Fitting | #532×C67 | C2 |
| hypercenter | #532 | D67 |
| hypocenter | C67 | D4×#41 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
1648 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|e^2=f,b^a=bf,c^a=cg,d^b=df,h^c=h^66,h^d=h^66974 conjugacy classes — view the full character table.
| maximal subgroup of | #30747850, #30747854, #30822689, … |
| maximal normal subgroup of | #30747850, #30747854, #30822689, … |
| maximal quotient of | #31015032, #31015142, #31015232, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17996);