Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ C2×#346 |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bg,h^a=h^9,h^c=h^16,h^d=h^13,h^f=h^16112 conjugacy classes — view the full character table.
| maximal subgroup of | #17981198, #17981250, #17981259, … |
| maximal normal subgroup of | #17981198, #17981250, #17981259, … |
| maximal quotient of | #17981817, #17981828, #17981843, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21666);