Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ #1296 |
188 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,c^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^16,c^b=cg358 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1296, C2×#14526668, #16924409, … |
| maximal normal subgroup of | D17×#1296, C2×#14526668, #16924409, … |
| maximal quotient of | #16920876, #16920892, #16920893, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2394);