Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C17 ⋊ C8 |
| Sylow | C17 ⋊ #1278 |
172 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 55 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,c^2=f,d^2=g,e^2=g,b^a=bc,c^a=cf,e^a=ef,h^a=h^2,h^b=h^9,h^d=h^4,h^e=h^13,h^g=h^1676 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14545791, #17981574, #17981613, … |
| maximal normal subgroup of | C2×#14545791, #17981574, #17981613, … |
| maximal quotient of | #17981067, #17981075, #17981077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21517);