Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×Dic17 |
| derived, Sylow | C17 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D17 |
| commutator, hypocenter | C17 | C23×C4 |
| Frattini | C2 | C23×D17 |
| Fitting, socle, prime radical | C24×C17 | C2 |
| cosocle | C2×C17 | C24 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C24 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10587502, C22⋊C4×Dic17, #11762667, … |
| maximal normal subgroup of | C2×#10587502, C22⋊C4×Dic17, #11762667, … |
| maximal quotient of | C22×C4×Dic17, C22×C22⋊Dic17, C22×C4⋊Dic17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 234);