Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C71 ⋊ #20691 |
1266 conjugacy classes of subgroups; only the 395 normal subgroups are shown.
This group has 1266 conjugacy classes of subgroups — too many to draw. Only its 395 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|a^2=g,b^2=h,c^2=e,d^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^70,d^b=dh,g^c=gh2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 169320);