Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #101×C37 ⋊ C2 |
| Sylow | C37 ⋊ #454 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^36,d^b=df,e^b=ef,g^b=g^36,d^c=df214 conjugacy classes — view the full character table.
| maximal subgroup of | #17996614, #17996618, #17996623, … |
| maximal normal subgroup of | #17996614, #17996618, #17996623, … |
| maximal quotient of | #17993527, #17993533, #17993538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 724);