Finite Group DatabasebetaFinite Group Databasebeta| order | 17456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D1091)⋊C4 |
| Fitting | C2×C4×C1091 ⋊ C2 |
| Sylow | C1091 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8728 |
Polycyclic presentation:
2^4,1091|a^2=d,b^a=bc,e^b=e^10904370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D1091, C2×(C2×D1091)⋊C4, #46853391, … |
| maximal normal subgroup of | C22⋊C4×D1091, C2×(C2×D1091)⋊C4, #46853391, … |
| maximal quotient of | C1091⋊#95, (C2×D1091)⋊C8, #46853348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17456, 17);