Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #431×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1460 |
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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,c^2=fg,e^2=g,b^a=bd,d^a=df,e^b=ef,h^b=h^661364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30746388, C8×#14523959, #30746398, … |
| maximal normal subgroup of | #30746388, C8×#14523959, #30746398, … |
| maximal quotient of | #30743798, #30743805, #30743812, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2830);