Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C17×#322 ⋊ C2 |
| Sylow | C17 ⋊ C8×M16 |
224 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 121 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=d,b^2=e,d^2=f,e^2=g,c^a=cf,h^b=h^16,h^c=h^16400 conjugacy classes — view the full character table.
| maximal subgroup of | C8×M16×D17, C2×#14527063, #16999905, … |
| maximal normal subgroup of | C8×M16×D17, C2×#14527063, #16999905, … |
| maximal quotient of | #16923676, #16923704, #16924748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2789);