Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ #1390 |
234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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,b^a=bc,c^a=cf,f^a=fg,h^a=h^16,d^b=df,d^c=dg250 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1390, C2×#14526902, #16949265, … |
| maximal normal subgroup of | D17×#1390, C2×#14526902, #16949265, … |
| maximal quotient of | #16921283, #16921319, #16921322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2628);