Finite Group DatabasebetaFinite Group Databasebeta| order | 18992 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic1187⋊C4 |
| Sylow | C1187 ⋊ C4⋊C4 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18992 |
Polycyclic presentation:
2^4,1187|a^2=d,b^2=c,b^a=bc,e^b=e^11864754 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4⋊C4×D1187, C2×Dic1187⋊C4, #49184210, … |
| maximal normal subgroup of | C4⋊C4×D1187, C2×Dic1187⋊C4, #49184210, … |
| maximal quotient of | C1187⋊#95, Dic1187⋊C8, #49184185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18992, 19);