Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C17 ⋊ #1692 |
146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 146 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) = 2176 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=d,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^16,c^b=cf,h^b=h^16,e^c=eg175 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1692, C2×#14528292, #17016962, … |
| maximal normal subgroup of | D17×#1692, C2×#14528292, #17016962, … |
| maximal quotient of | #16927411, #16930528, #16930538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4018);