Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C8×D4×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3287 |
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|b^2=g,c^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^66,d^b=de,e^b=eg,h^b=h^66,e^d=eg,h^d=h^661355 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30769260, #30769264, #30769288, … |
| maximal normal subgroup of | #30769260, #30769264, #30769288, … |
| maximal quotient of | #30846860, #30846875, #30846890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 16270);