Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #1326 |
158 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 34 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,d^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^13,c^b=cg,d^b=de,h^b=h^16,d^c=dg,h^d=h^16154 conjugacy classes — view the full character table.
| maximal subgroup of | #17958212, C2×#14543729, #17958215, … |
| maximal normal subgroup of | #17958212, C2×#14543729, #17958215, … |
| maximal quotient of | #17948345, #17948351, #17948458, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19455);