Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #2153 |
152 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 72 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=e,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^13,c^b=cg,h^c=h^16,h^e=h^16124 conjugacy classes — view the full character table.
| maximal subgroup of | #17960030, #17960033, #17960036, … |
| maximal normal subgroup of | #17960030, #17960033, #17960036, … |
| maximal quotient of | #17960059, #17960085, #17960115, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20852);