Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #2361 |
788 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=eg,d^2=e,b^a=be,c^a=cf,h^a=h^16,d^b=de,h^c=h^16370 conjugacy classes — view the full character table.
| maximal subgroup of | #17054591, #17054598, #17054636, … |
| maximal normal subgroup of | #17054591, #17054598, #17054636, … |
| maximal quotient of | C4⋊C4×#63227, #16955823, #16955892, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7528);