Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×M16×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×H(3,ℤ/4) |
404 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=f,d^2=g,b^a=bd,f^a=fg,h^a=h^4,e^b=eg,h^b=h^13,h^c=h^16,h^e=h^16,h^f=h^16124 conjugacy classes — view the full character table.
| maximal subgroup of | #17948874, #17948882, H(3,ℤ/4)×#595, … |
| maximal normal subgroup of | #17948874, #17948882, H(3,ℤ/4)×#595, … |
| maximal quotient of | #17950314, #17950318, #17950321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20182);