Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×M16×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3183 |
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^66,c^b=cg,d^c=dg1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30766670, #30766674, #31011079, … |
| maximal normal subgroup of | #30766670, #30766674, #31011079, … |
| maximal quotient of | #30856436, #30860148, #30860159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15239);