Finite Group DatabasebetaFinite Group Databasebeta| order | 17872 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic1117 |
| Sylow | C1117 ⋊ C4⋊C4 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17872 |
Polycyclic presentation:
2^4,1117|a^2=d,b^2=c,b^a=bc,e^a=e^11164474 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49088453, #49088454, #49088456, … |
| maximal normal subgroup of | #49088453, #49088454, #49088456, … |
| maximal quotient of | #49088439, C4⋊#22582039, #49088464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17872, 20);