Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q16×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2947 |
470 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=f,b^2=g,c^2=f,e^2=g,b^a=be,e^a=eg,e^b=eg,d^c=dg,h^c=h^66,h^d=h^66968 conjugacy classes — view the full character table.
| maximal subgroup of | #2947×D67, C2×#22569047, #31719945, … |
| maximal normal subgroup of | #2947×D67, C2×#22569047, #31719945, … |
| maximal quotient of | #30825275, #30825466, #30825495, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13348);