Finite Group DatabasebetaFinite Group Databasebeta| order | 17456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C1091 ⋊ Q16 |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17456 |
Polycyclic presentation:
2^4,1091|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^10902732 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q16×D1091, C2×#31775398, #46853454, … |
| maximal normal subgroup of | Q16×D1091, C2×#31775398, #46853454, … |
| maximal quotient of | #46853357, #46853358, #46853367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17456, 30);