Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ C8×#41 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,h^a=h^4,h^c=h^13,h^d=h^16,h^f=h^16160 conjugacy classes — view the full character table.
| maximal subgroup of | #17951932, #17951938, #17951944, … |
| maximal normal subgroup of | #17951932, #17951938, #17951944, … |
| maximal quotient of | #17968674, #17968676, C4×D4×#3624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21315);