Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ #2931 |
500 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 170 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=f,c^2=f,f^2=g,b^a=be,d^a=dg,h^a=h^4,d^b=dg,h^b=h^16,h^c=h^13,h^d=h^16,h^f=h^16112 conjugacy classes — view the full character table.
| maximal subgroup of | #17952162, #17952171, #17952180, … |
| maximal normal subgroup of | #17952162, #17952171, #17952180, … |
| maximal quotient of | #17967223, #17967228, #17967232, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21235);