Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #131×C37 ⋊ C2 |
| Sylow | C37 ⋊ #472 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^36,e^c=ef376 conjugacy classes — view the full character table.
| maximal subgroup of | #17996553, #17996555, #17996560, … |
| maximal normal subgroup of | #17996553, #17996555, #17996560, … |
| maximal quotient of | #17993951, #17993956, #17993995, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 819);