Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ Q8×C16 |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,h^a=h^8,h^c=h^9,h^e=h^13,h^f=h^16100 conjugacy classes — view the full character table.
| maximal subgroup of | #17982297, #17982299, #17982305, … |
| maximal normal subgroup of | #17982297, #17982299, #17982305, … |
| maximal quotient of | C4⋊C4×#63241, #17982473, #17982627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21734);