Finite Group DatabasebetaFinite Group Databasebeta| order | 17552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#17984203 |
| Fitting | C4×C1097 ⋊ C4 |
| Sylow | C1097 ⋊ C4⋊C4 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4388 |
Polycyclic presentation:
2^4,1097|a^2=d,b^2=c,b^a=bc,e^a=e^341,e^d=e^10961106 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47975544, #47975545, #47975550, … |
| maximal normal subgroup of | #47975544, #47975545, #47975550, … |
| maximal quotient of | (C2×#17984203)⋊C4, C4⋊#22578595, #47975549, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17552, 46);