Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4×Q8×C17 ⋊ C2 |
| Sylow | C17 ⋊ #2426 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^16358 conjugacy classes — view the full character table.
| maximal subgroup of | #17081706, #17081711, #17081751, … |
| maximal normal subgroup of | #17081706, #17081711, #17081751, … |
| maximal quotient of | #16956258, #16956828, #16957112, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 8070);