Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C17 ⋊ C2 |
| Sylow | C17 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^5,17|b^2=c,c^2=e,b^a=bd,f^a=f^16148 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C8×D17, C2×#10587491, #11762771, … |
| maximal normal subgroup of | C22⋊C8×D17, C2×#10587491, #11762771, … |
| maximal quotient of | #11762532, #11762534, #11762536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 27);