Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C37 ⋊ C4 |
| Sylow | C37 ⋊ #365 |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=d,b^2=c,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^6,d^b=df,g^d=g^36160 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14558458, D37⋊#365, #18010943, … |
| maximal normal subgroup of | C2×#14558458, D37⋊#365, #18010943, … |
| maximal quotient of | #18009621, #18009622, #18009661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1474);