Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q8×C67 ⋊ C2 |
| Sylow | C67 ⋊ #137 |
60 conjugacy classes of subgroups.
| 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=de341 conjugacy classes — view the full character table.
| maximal subgroup of | #16863572, #16863573, #16863577, … |
| maximal normal subgroup of | #16863572, #16863573, #16863577, … |
| maximal quotient of | #16863395, #16863405, #16863436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 177);