Finite Group DatabasebetaFinite Group Databasebeta| order | 17456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic2182 |
| unambiguous semidirect product | (C2×C1091)⋊Q8 |
| Sylow | C1091 ⋊ C2×Q8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17456 |
4370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46853352, #46853357, #46853359, … |
| maximal normal subgroup of | #46853352, #46853357, #46853359, … |
| maximal quotient of | C2×Dic1091⋊C4, C2×C4⋊Dic1091, C4×Dic2182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17456, 38);