Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C17×C32 ⋊ C4 |
| 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,c^b=cg,h^b=h^13,h^d=h^16172 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14543893, #17962557, #17962561, … |
| maximal normal subgroup of | C2×#14543893, #17962557, #17962561, … |
| maximal quotient of | #17949091, #17949099, #17949393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19619);