Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #108×C37 ⋊ C2 |
| Sylow | C37 ⋊ #473 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=f,b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^36,e^c=ef,g^c=g^36268 conjugacy classes — view the full character table.
| maximal subgroup of | #17996568, #17996570, #17996575, … |
| maximal normal subgroup of | #17996568, #17996570, #17996575, … |
| maximal quotient of | #17993962, #17993967, #17993986, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 825);