Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D8×C37 ⋊ C2 |
| Sylow | C37 ⋊ #509 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^36,d^b=de,e^b=ef268 conjugacy classes — view the full character table.
| maximal subgroup of | #17996492, #17996497, #17996540, … |
| maximal normal subgroup of | #17996492, #17996497, #17996540, … |
| maximal quotient of | #17996306, #17996312, #17996382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 985);