Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×#435 ⋊ C2 |
| Sylow | C17 ⋊ #3313 |
380 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=g,c^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^16,c^b=cg,d^b=de,f^c=fg,h^c=h^16253 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3313, C2×#14540852, #17911101, … |
| maximal normal subgroup of | D17×#3313, C2×#14540852, #17911101, … |
| maximal quotient of | #17049911, #17050659, #17051457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 16578);