Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M16×C17 ⋊ C2 |
| Sylow | C17 ⋊ #100 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 136 |
Polycyclic presentation:
2^5,17|b^2=c,c^2=e,b^a=bd,c^a=ce,f^a=f^16,d^b=de91 conjugacy classes — view the full character table.
| maximal subgroup of | #100×D17, C2×#10587494, #11762791, … |
| maximal normal subgroup of | #100×D17, C2×#10587494, #11762791, … |
| maximal quotient of | #11762532, #11762548, #11762552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 30);