Finite Group DatabasebetaFinite Group Databasebeta| order | 18736 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊Dic1171 |
| Sylow | C1171 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9368 |
Polycyclic presentation:
2^4,1171|a^2=d,b^a=bc,e^a=e^11704690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49153972, #49153973, C22⋊C4×D1171, … |
| maximal normal subgroup of | #49153972, #49153973, C22⋊C4×D1171, … |
| maximal quotient of | C1171⋊#95, C22⋊(C1171⋊C8), #49153973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18736, 18);