Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D37⋊M32 |
| Sylow | C37 ⋊ C2×M32 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^31,g^c=g^36,g^d=g^36184 conjugacy classes — view the full character table.
| maximal subgroup of | #18009639, #18009642, #18009645, … |
| maximal normal subgroup of | #18009639, #18009642, #18009645, … |
| maximal quotient of | #18010797, #18010802, #18010803, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1605);