Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C4×C37 ⋊ C4 |
| Sylow | C37 ⋊ #381 |
218 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=f,c^2=d,b^a=bd,c^a=ce,g^a=g^31,g^f=g^36172 conjugacy classes — view the full character table.
| maximal subgroup of | #18009444, #18009445, #18009500, … |
| maximal normal subgroup of | #18009444, #18009445, #18009500, … |
| maximal quotient of | #18009770, #18009772, #18009780, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1492);