Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C37 ⋊ #356 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=d,b^2=f,c^2=f,d^2=f,b^a=bc,c^a=ce,e^a=ef,c^b=cf,d^b=def,g^b=g^36,d^c=df211 conjugacy classes — view the full character table.
| maximal subgroup of | #356×D37, C2×#14557331, #17996278, … |
| maximal normal subgroup of | #356×D37, C2×#14557331, #17996278, … |
| maximal quotient of | #17992529, #17992541, #17992601, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 347);