Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #1642 |
250 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,c^2=fg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^16,d^b=df,e^b=eg,d^c=dg,e^c=eg226 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1642, C2×#14527984, #17010258, … |
| maximal normal subgroup of | D17×#1642, C2×#14527984, #17010258, … |
| maximal quotient of | #16923264, #16923278, #16923292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 3710);