Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×#108×C67 ⋊ C2 |
| Sylow | C67 ⋊ #12640 |
442 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8576 |
Polycyclic presentation:
2^8,67|a^2=e,b^2=f,c^2=e,d^2=gh,f^2=gh,g^2=h,b^a=bd,d^a=dg,f^a=fgh,g^a=gh,i^a=i^66,c^b=ch,i^b=i^661912 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 84800);