Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #1927 |
254 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 93 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=f,b^2=dfg,c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^66,h^b=h^66,e^c=eg,h^c=h^66962 conjugacy classes — view the full character table.
| maximal subgroup of | #1927×D67, C2×#22560846, #30858227, … |
| maximal normal subgroup of | #1927×D67, C2×#22560846, #30858227, … |
| maximal quotient of | #30754021, #30754049, #30754175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5147);