Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #99 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 136 |
Polycyclic presentation:
2^5,17|b^2=c,b^a=bd,c^a=ce,f^a=f^16,d^b=de91 conjugacy classes — view the full character table.
| maximal subgroup of | #99×D17, C2×#10587477, #11762781, … |
| maximal normal subgroup of | #99×D17, C2×#10587477, #11762781, … |
| maximal quotient of | #11762532, #11762534, #11762542, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 13);