Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ #2659 |
524 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 165 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,b^2=g,c^2=f,b^a=be,c^a=cf,c^b=cg,h^b=h^16,d^c=de256 conjugacy classes — view the full character table.
| maximal subgroup of | #16934877, #16934879, #16934882, … |
| maximal normal subgroup of | #16934877, #16934879, #16934882, … |
| maximal quotient of | #16960862, #16960919, #16960920, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 10626);