Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#41×C17 ⋊ C4 |
| Sylow | C17 ⋊ #1788 |
612 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 94 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,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^13,d^b=dg,h^f=h^16118 conjugacy classes — view the full character table.
| maximal subgroup of | #17952876, #17952877, #17952878, … |
| maximal normal subgroup of | #17952876, #17952877, #17952878, … |
| maximal quotient of | #17952472, #17952473, #17952474, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20350);