Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C17×#386 ⋊ C2 |
| Sylow | C17 ⋊ D4×C22⋊C4 |
1252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=g,b^a=be,c^a=cf,d^b=de,h^c=h^16,h^d=h^16274 conjugacy classes — view the full character table.
| maximal subgroup of | D4×C22⋊C4×D17, C2×#14531602, #17193524, … |
| maximal normal subgroup of | D4×C22⋊C4×D17, C2×#14531602, #17193524, … |
| maximal quotient of | #16955723, #16955725, #16955738, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7328);