Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#22575824 |
| Sylow | C541 ⋊ C2×SD16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
2714 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22575824, #46830266, #46830272, … |
| maximal normal subgroup of | C4×#22575824, #46830266, #46830272, … |
| maximal quotient of | C2×#31772549, C2×#31772551, C2×#31772559, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 160);