Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C17 ⋊ #1453 |
190 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,d^2=f,e^2=g,c^a=cg,h^a=h^4,c^b=cf,h^b=h^13,h^d=h^16,h^e=h^16136 conjugacy classes — view the full character table.
| maximal subgroup of | #17948786, #17948789, #17958974, … |
| maximal normal subgroup of | #17948786, #17948789, #17958974, … |
| maximal quotient of | #17950285, #17950307, #17951695, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19729);