Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C17 ⋊ C8 |
| Sylow | C17 ⋊ #1565 |
180 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 71 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=e,b^2=d,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^9,c^b=cf,h^e=h^13,h^g=h^1664 conjugacy classes — view the full character table.
| maximal subgroup of | #17981693, #17981694, #17981695, … |
| maximal normal subgroup of | #17981693, #17981694, #17981695, … |
| maximal quotient of | #17981572, #17981631, #17981663, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21635);