Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #1395 |
162 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 38 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,e^2=g,b^a=bc,c^a=cf,e^a=eg,f^a=fg,d^b=dfg,h^b=h^13,d^c=dg,h^e=h^1670 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14543883, #17960637, #17960643, … |
| maximal normal subgroup of | C2×#14543883, #17960637, #17960643, … |
| maximal quotient of | #17948658, #17948710, #17948711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19609);