Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ #2906 |
484 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 204 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=f,b^2=e,f^2=g,b^a=be,h^a=h^13,h^b=h^16,d^c=dg,h^c=h^16,h^d=h^16,h^f=h^16130 conjugacy classes — view the full character table.
| maximal subgroup of | #17954781, #17954785, #17954789, … |
| maximal normal subgroup of | #17954781, #17954785, #17954789, … |
| maximal quotient of | #17966491, #17966497, #17966501, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21158);