Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #1980 |
336 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 93 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=df,c^2=e,d^2=g,b^a=bd,c^a=ce,d^b=dg,f^b=fg,h^b=h^16358 conjugacy classes — view the full character table.
| maximal subgroup of | #16926204, #16926207, #16926225, … |
| maximal normal subgroup of | #16926204, #16926207, #16926225, … |
| maximal quotient of | #16933275, #16933279, #16933283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 5428);