Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C37 ⋊ C2 |
| Sylow | C37 ⋊ #349 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=d,d^2=e,e^2=f,b^a=bc,c^a=cf,d^b=df,g^b=g^36382 conjugacy classes — view the full character table.
| maximal subgroup of | #349×D37, C2×#14557314, #17996215, … |
| maximal normal subgroup of | #349×D37, C2×#14557314, #17996215, … |
| maximal quotient of | #17992519, #17992535, #17992553, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 330);