Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #1383 |
136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,c^2=f,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,d^b=dg,h^b=h^13,h^e=h^1688 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14543848, #17960524, #17960934, … |
| maximal normal subgroup of | C2×#14543848, #17960524, #17960934, … |
| maximal quotient of | #17948545, #17948603, #17948608, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19574);