Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D541⋊M16 |
| Sylow | C541 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4328 |
Polycyclic presentation:
2^5,541|a^2=d,d^2=e,b^a=be,f^a=f^52,f^c=f^540,f^d=f^5401100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46831042, #46831044, #46831046, … |
| maximal normal subgroup of | #46831042, #46831044, #46831046, … |
| maximal quotient of | #46831134, C4×#22575845, C4×#22575846, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 231);