Finite Group DatabasebetaFinite Group Databasebeta| order | 18992 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊Dic1187 |
| Sylow | C1187 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9496 |
Polycyclic presentation:
2^4,1187|a^2=d,b^a=bc,e^a=e^11864754 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49184168, #49184169, C22⋊C4×D1187, … |
| maximal normal subgroup of | #49184168, #49184169, C22⋊C4×D1187, … |
| maximal quotient of | C1187⋊#95, C22⋊(C1187⋊C8), #49184169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18992, 18);