Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #106×C37 ⋊ C2 |
| Sylow | C37 ⋊ #360 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=d,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,c^b=cef,d^b=df,e^b=ef,g^b=g^36268 conjugacy classes — view the full character table.
| maximal subgroup of | #360×D37, C2×#14557342, #17996330, … |
| maximal normal subgroup of | #360×D37, C2×#14557342, #17996330, … |
| maximal quotient of | #17992562, #17992565, #17992604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 358);