Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C37 ⋊ #365 |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=d,b^2=c,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^36,d^b=df,g^b=g^36268 conjugacy classes — view the full character table.
| maximal subgroup of | #365×D37, C2×#14557357, #17996367, … |
| maximal normal subgroup of | #365×D37, C2×#14557357, #17996367, … |
| maximal quotient of | #17992661, #17992696, C2×#14557357 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 373);