Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ #3407 |
360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=e,e^2=f,f^2=g,d^a=dg,h^a=h^9,c^b=cg,h^b=h^16,h^c=h^16,h^e=h^13,h^f=h^1688 conjugacy classes — view the full character table.
| maximal subgroup of | #17982575, #17982603, #17982605, … |
| maximal normal subgroup of | #17982575, #17982603, #17982605, … |
| maximal quotient of | #17983015, #17983021, #17983037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21765);