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 ⋊ #2947 |
470 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=g,c^2=f,e^2=g,b^a=be,e^a=eg,h^a=h^4,e^b=eg,d^c=dg,h^c=h^13,h^f=h^1688 conjugacy classes — view the full character table.
| maximal subgroup of | #17976104, #17976106, #17976108, … |
| maximal normal subgroup of | #17976104, #17976106, #17976108, … |
| maximal quotient of | #17966632, #17966633, #17966634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21268);