Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D17 |
| unambiguous semidirect product | C17⋊C25 |
| unambiguous semidirect product | (C2×C17)⋊C24 |
| Fitting, socle | C24×C17 ⋊ C2 |
| derived, Sylow | C17 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D17 |
| commutator, cosocle, hypocenter | C17 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C17 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #11762664, C2×C22⋊C4×D17, C22×#63227, … |
| maximal normal subgroup of | #11762664, C2×C22⋊C4×D17, C22×#63227, … |
| maximal quotient of | C23×C4×D17, C24×Dic17, C22×D4×D17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 245);