Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #427×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3341 |
364 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|a^2=eg,b^2=g,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,h^b=h^66,f^c=fg959 conjugacy classes — view the full character table.
| maximal subgroup of | #31012765, #31012767, #31012787, … |
| maximal normal subgroup of | #31012765, #31012767, #31012787, … |
| maximal quotient of | #30872093, #30873487, #30873491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 16930);