Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C17 ⋊ #1398 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bf,d^a=dg,h^a=h^9,c^b=cg,h^b=h^4,h^c=h^13,h^d=h^16,h^e=h^1676 conjugacy classes — view the full character table.
| maximal subgroup of | #17981349, #17981350, #17981435, … |
| maximal normal subgroup of | #17981349, #17981350, #17981435, … |
| maximal quotient of | #17981340, #17981345, #17981472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21600);