Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C37 ⋊ #368 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=d,b^2=ce,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^b=g^36274 conjugacy classes — view the full character table.
| maximal subgroup of | #368×D37, C2×#14557362, #17996389, … |
| maximal normal subgroup of | #368×D37, C2×#14557362, #17996389, … |
| maximal quotient of | #17992667, #17992669, #17992689, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 378);