Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D37⋊#101 |
| Sylow | C37 ⋊ C2×#101 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=e,b^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^31,e^b=ef,g^c=g^36,g^e=g^36112 conjugacy classes — view the full character table.
| maximal subgroup of | #18009692, #101×#3866, #18010443, … |
| maximal normal subgroup of | #18009692, #101×#3866, #18010443, … |
| maximal quotient of | D37⋊#324, #18009839, #18009840, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1534);