Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#123 ⋊ C4 |
| Sylow | C17 ⋊ #2359 |
652 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=g,c^2=e,b^a=be,c^a=cf,h^a=h^4,d^b=de,h^b=h^13,h^g=h^16106 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14545307, #17979003, #17979016, … |
| maximal normal subgroup of | C2×#14545307, #17979003, #17979016, … |
| maximal quotient of | #17963019, #17963047, #17963049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21033);