Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C4×C17 ⋊ C8 |
| Sylow | C17 ⋊ #1282 |
228 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 136 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,d^2=g,e^2=g,b^a=bc,c^a=cf,h^a=h^2,d^b=df,h^b=h^9,h^d=h^4,h^e=h^13,h^g=h^1664 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14545795, #17981586, #99×#3633, … |
| maximal normal subgroup of | C2×#14545795, #17981586, #99×#3633, … |
| maximal quotient of | #17981069, #17981075, #17981078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21521);