Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ #2398 |
568 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 161 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=e,b^2=e,d^2=ef,b^a=be,c^a=cf,c^b=cg,h^b=h^16364 conjugacy classes — view the full character table.
| maximal subgroup of | #16929391, #16929393, #16929405, … |
| maximal normal subgroup of | #16929391, #16929393, #16929405, … |
| maximal quotient of | #16956027, #16956062, #16956081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7794);