Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C17×#386 ⋊ C2 |
| Sylow | C17 ⋊ #2380 |
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,h^d=h^16262 conjugacy classes — view the full character table.
| maximal subgroup of | #16951126, #16951129, #16951633, … |
| maximal normal subgroup of | #16951126, #16951129, #16951633, … |
| maximal quotient of | #16955949, #16955962, #16955963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7685);