Finite Group DatabasebetaFinite Group Databasebeta| order | 17872 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C1117 ⋊ SD16 |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8936 |
Polycyclic presentation:
2^4,1117|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1116,c^b=cd2797 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D1117, C2×#31821898, #49088551, … |
| maximal normal subgroup of | SD16×D1117, C2×#31821898, #49088551, … |
| maximal quotient of | #49088453, #49088455, #49088463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17872, 28);