Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×D8×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3273 |
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^66,c^b=cg,d^b=de,e^b=eg,h^c=h^66,e^d=eg953 conjugacy classes — view the full character table.
| maximal subgroup of | #30769310, #30769314, #30769324, … |
| maximal normal subgroup of | #30769310, #30769314, #30769324, … |
| maximal quotient of | #30847108, #30847192, #30847308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 16120);