Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #2171 |
144 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 144 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.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=e,c^2=e,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=cg,d^a=dg,h^a=h^9,d^b=dg,h^c=h^9,h^e=h^13,h^f=h^1658 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14546004, #17983177, #17983178, … |
| maximal normal subgroup of | C2×#14546004, #17983177, #17983178, … |
| maximal quotient of | #17982277, #17982280, #17982300, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21730);