Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C17×C4⋊C8 ⋊ C4 |
| Sylow | C17 ⋊ C8×C4⋊C4 |
296 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 124 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=e,b^2=f,c^2=de,e^2=g,b^a=bd,h^a=h^4,h^b=h^4,h^c=h^13,h^e=h^16,h^f=h^16160 conjugacy classes — view the full character table.
| maximal subgroup of | #17951981, #17951985, #17951989, … |
| maximal normal subgroup of | #17951981, #17951985, #17951989, … |
| maximal quotient of | C4⋊C8×#3624, #17952261, #17952268, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20303);