Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C67 ⋊ C2 |
| Sylow | C67 ⋊ #137 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1072 |
Polycyclic presentation:
2^5,67|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^66,d^b=de,f^c=f^66242 conjugacy classes — view the full character table.
| maximal subgroup of | #137×D67, C2×#14524075, #16864193, … |
| maximal normal subgroup of | #137×D67, C2×#14524075, #16864193, … |
| maximal quotient of | #16863396, #16863403, #16863437, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 178);