Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C71 ⋊ #20579 |
5990 conjugacy classes of subgroups; only the 699 normal subgroups are shown.
This group has 5990 conjugacy classes of subgroups — too many to draw. Only its 699 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2272 |
Polycyclic presentation:
2^8,71|a^2=g,g^2=h,b^a=be,c^a=cf,d^a=dh,i^a=i^704568 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 168678);