Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C17×#131 ⋊ C4 |
| Sylow | C17 ⋊ #1814 |
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 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=f,b^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^13,e^c=eg,f^c=fg,h^f=h^16112 conjugacy classes — view the full character table.
| maximal subgroup of | #17961290, #17961291, #17961501, … |
| maximal normal subgroup of | #17961290, #17961291, #17961501, … |
| maximal quotient of | #17953286, #17953287, #17953292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20396);