Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #322×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1588 |
166 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 63 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=e,b^2=f,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,h^a=h^66,d^b=df,h^b=h^661358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1588×D67, C2×#22559089, #30825398, … |
| maximal normal subgroup of | #1588×D67, C2×#22559089, #30825398, … |
| maximal quotient of | #30746644, #30746693, #30747102, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 3390);