Finite Group DatabasebetaFinite Group Databasebeta| order | 17744 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q8×C1109 ⋊ C2 |
| Sylow | C1109 ⋊ SD16 |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8872 |
Polycyclic presentation:
2^4,1109|a^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^11082777 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D1109, C2×#31801552, #48000562, … |
| maximal normal subgroup of | SD16×D1109, C2×#31801552, #48000562, … |
| maximal quotient of | #48000462, #48000466, #48000473, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17744, 27);