Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ #3202 |
378 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 117 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=g,b^2=g,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^16,c^b=ce,d^b=dg,f^c=fg,h^c=h^16250 conjugacy classes — view the full character table.
| maximal subgroup of | #16946459, #16946462, #16946476, … |
| maximal normal subgroup of | #16946459, #16946462, #16946476, … |
| maximal quotient of | #17043432, #17044639, #17045637, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 15405);