Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ C2×#347 |
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,h^a=h^13,d^b=dg,h^c=h^16,h^d=h^16124 conjugacy classes — view the full character table.
| maximal subgroup of | #17948912, #17948917, D17⋊#1355, … |
| maximal normal subgroup of | #17948912, #17948917, D17⋊#1355, … |
| maximal quotient of | #17958013, #17958020, #17958074, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20727);