Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×Q8×C17 ⋊ C4 |
| Sylow | C17 ⋊ #2295 |
500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=fg,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^4,h^b=h^13,h^g=h^16136 conjugacy classes — view the full character table.
| maximal subgroup of | #17951880, #17951886, #17951892, … |
| maximal normal subgroup of | #17951880, #17951886, #17951892, … |
| maximal quotient of | #17962928, #17962936, C4×#11763758, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20969);