Finite Group DatabasebetaFinite Group Databasebeta| order | 532 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×Dic7 |
| unambiguous semidirect product | C7⋊(C4×C19) |
| derived, Sylow | C7 ⋊ C4×C19 |
| Hall | C7×C19 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | D7 |
| commutator, hypocenter | C7 | C4×C19 |
| Frattini | C2 | D7×C19 |
| Fitting, socle, prime radical | C2×C7×C19 | C2 |
| cosocle | C2×C7 | C2×C19 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C19 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 532 |
190 conjugacy classes — view the full character table.
| maximal subgroup of | Dic7×D19, D133⋊C4, #11761534, … |
| maximal normal subgroup of | Dic7×D19, D133⋊C4, #11761534, … |
| maximal quotient of | C19×C7⋊C8, C2×C19×Dic7, C3×C19×Dic7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(532, 1);