Finite Group DatabasebetaFinite Group Databasebeta| order | 17872 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C1117 ⋊ Q16 |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17872 |
Polycyclic presentation:
2^4,1117|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^11162797 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q16×D1117, C2×#31821900, #49088552, … |
| maximal normal subgroup of | Q16×D1117, C2×#31821900, #49088552, … |
| maximal quotient of | #49088455, #49088456, #49088465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17872, 30);