Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C17 ⋊ #1328 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^9,c^b=cg,d^b=de,d^c=dg,h^d=h^13,h^f=h^1646 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14545825, #17981935, #17981936, … |
| maximal normal subgroup of | C2×#14545825, #17981935, #17981936, … |
| maximal quotient of | #17981115, #17981116, #17981117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21551);