Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #101×C37 ⋊ C2 |
| Sylow | C37 ⋊ #413 |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=e,c^2=f,e^2=f,b^a=bd,d^a=df,e^b=ef,g^b=g^36,g^c=g^36220 conjugacy classes — view the full character table.
| maximal subgroup of | #17996278, #17996280, #17996286, … |
| maximal normal subgroup of | #17996278, #17996280, #17996286, … |
| maximal quotient of | #17992909, #17992913, #17992929, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 532);