Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×#376×C71 ⋊ C2 |
| Sylow | C71 ⋊ #34639 |
1738 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 1738 conjugacy classes of subgroups — too many to draw. Only its 587 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9088 |
Polycyclic presentation:
2^8,71|b^2=fg,c^2=f,e^2=h,b^a=bf,c^a=cg,d^a=dh,i^a=i^70,c^b=ch2864 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 336916);