Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| isoclinism | isoclinic class of #63243 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#595 |
| unambiguous semidirect product | D17⋊(C22⋊C4) |
| unambiguous semidirect product | (C2×#595)⋊C22 |
| Fitting | C23×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×C22⋊C4 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 136 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | #11763686, #11763687, C4×C22⋊#595, … |
| maximal normal subgroup of | #11763686, #11763687, C4×C22⋊#595, … |
| maximal quotient of | C2×(C2×#595)⋊C4, C4×C22⋊#595, #11763750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 220);