Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C42×C37 ⋊ C4 |
| Sylow | C37 ⋊ #339 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 296 |
Polycyclic presentation:
2^6,37|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^31,g^d=g^36172 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14558404, #18010277, #104×#3866, … |
| maximal normal subgroup of | C2×#14558404, #18010277, #104×#3866, … |
| maximal quotient of | #18009424, #18009428, #18009431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1420);