Finite Group DatabasebetaFinite Group Databasebeta| order | 17648 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic1103 |
| Sylow | C1103 ⋊ C4⋊C4 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17648 |
Polycyclic presentation:
2^4,1103|a^2=d,b^2=c,b^a=bc,e^a=e^11024418 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47976941, #47976942, #47976944, … |
| maximal normal subgroup of | #47976941, #47976942, #47976944, … |
| maximal quotient of | C1103⋊#95, C4⋊(C1103⋊C8), #47976952, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17648, 20);