Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #1376 |
148 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=cg,e^a=eg,h^a=h^9,h^b=h^4,h^d=h^13,h^e=h^16,h^f=h^1688 conjugacy classes — view the full character table.
| maximal subgroup of | #17981161, #17981162, #17981169, … |
| maximal normal subgroup of | #17981161, #17981162, #17981169, … |
| maximal quotient of | #17981200, #17981212, #17981218, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21585);