Finite Group DatabasebetaFinite Group Databasebeta| order | 17392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D1087)⋊C4 |
| Fitting | C2×C4×C1087 ⋊ C2 |
| Sylow | C1087 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8696 |
Polycyclic presentation:
2^4,1087|a^2=d,b^a=bc,e^b=e^10864354 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D1087, C2×(C2×D1087)⋊C4, #46852145, … |
| maximal normal subgroup of | C22⋊C4×D1087, C2×(C2×D1087)⋊C4, #46852145, … |
| maximal quotient of | C1087⋊#95, (C2×D1087)⋊C8, #46852102, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17392, 17);