Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q32×C37 ⋊ C2 |
| Sylow | C37 ⋊ SD64 |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,c^b=cd,d^b=de,e^b=ef,g^b=g^36217 conjugacy classes — view the full character table.
| maximal subgroup of | SD64×D37, C2×#14557370, #17996903, … |
| maximal normal subgroup of | SD64×D37, C2×#14557370, #17996903, … |
| maximal quotient of | #17992773, #17992777, #17992797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 386);