Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C37 ⋊ C4 |
| Sylow | C37 ⋊ #347 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,c^b=cf,g^b=g^31,g^d=g^36166 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14558423, #18010811, #18010815, … |
| maximal normal subgroup of | C2×#14558423, #18010811, #18010815, … |
| maximal quotient of | #18009512, #18009515, #18009636, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1439);