Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C17×C22⋊Q8 ⋊ C2 |
| Sylow | C17 ⋊ #2488 |
546 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=f,c^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^16,c^b=cg,h^b=h^16,h^c=h^16262 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#2488, C2×#14533116, #17203364, … |
| maximal normal subgroup of | D17×#2488, C2×#14533116, #17203364, … |
| maximal quotient of | #16956256, #16956478, #16957400, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 8842);