Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#137 ⋊ C4 |
| Sylow | C17 ⋊ #2955 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^4,e^b=eg,h^b=h^16,h^c=h^13,h^f=h^1688 conjugacy classes — view the full character table.
| maximal subgroup of | #17971224, #17971225, #17971228, … |
| maximal normal subgroup of | #17971224, #17971225, #17971228, … |
| maximal quotient of | #17966616, #17966618, #17966619, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21283);