Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#131×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2955 |
456 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,h^b=h^661364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30772698, #30772699, #30772701, … |
| maximal normal subgroup of | #30772698, #30772699, #30772701, … |
| maximal quotient of | C8×#14524068, C8×#14524069, C8×#14524073, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13411);