Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C4×Q8×C17 ⋊ C2 |
| Sylow | C17 ⋊ #3523 |
992 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=f,d^2=f,e^2=fg,b^a=bf,c^a=cg,e^a=ef,h^a=h^16,d^b=df364 conjugacy classes — view the full character table.
| maximal subgroup of | #16926211, #16926215, #17001539, … |
| maximal normal subgroup of | #16926211, #16926215, #17001539, … |
| maximal quotient of | #17194564, #17195073, #17195190, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 18606);