Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#595 |
| unambiguous semidirect product | D17⋊C42 |
| Fitting | C2×C4×C17 ⋊ C4 |
| derived, Sylow | C17 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #595 |
| commutator, hypocenter | C17 | C2×C42 |
| Frattini | C2 | C22×#595 |
| Fitting | C2×C4×C17 | C4 |
| socle | C22×C17 | C2×C4 |
| prime radical | C22×D17 | C22 |
| cosocle | C2×D17 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 136 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | #11763674, #11763679, #11763681, … |
| maximal normal subgroup of | #11763674, #11763679, #11763681, … |
| maximal quotient of | C42×#595, C2×(C2×#595)⋊C4, #11763745, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 211);