Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C37 ⋊ #358 |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^6,37|a^2=d,b^2=f,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^36,c^b=ce,e^b=ef274 conjugacy classes — view the full character table.
| maximal subgroup of | #358×D37, C2×#14557337, #17996302, … |
| maximal normal subgroup of | #358×D37, C2×#14557337, #17996302, … |
| maximal quotient of | #17992560, #17992608, #17992645, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 353);