Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C17×#386 ⋊ C2 |
| Sylow | C17 ⋊ #2328 |
740 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=eg,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,h^d=h^16268 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#2328, C2×#14531505, #17193129, … |
| maximal normal subgroup of | D17×#2328, C2×#14531505, #17193129, … |
| maximal quotient of | #16955582, #16955627, #16955630, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7231);