Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C17 ⋊ C2 |
| Sylow | C17 ⋊ #137 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^5,17|b^2=e,c^2=e,d^2=e,c^a=ce,f^a=f^16,c^b=cd,d^b=de,d^c=de67 conjugacy classes — view the full character table.
| maximal subgroup of | #137×D17, C2×#10587604, #11763606, … |
| maximal normal subgroup of | #137×D17, C2×#10587604, #11763606, … |
| maximal quotient of | #11762809, #11762816, #11762850, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 140);