Finite Group DatabasebetaFinite Group Databasebeta| order | 572 |
| isoclinism | isoclinic class of D11×D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D13 |
| unambiguous semidirect product | (C13×D11)⋊C2 |
| unambiguous semidirect product | (C11×D13)⋊C2 |
| unambiguous semidirect product | D143⋊C2 |
| Fitting, socle, derived, Hall | C11×C13 ⋊ C22 |
| Sylow | C13 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C13 | C22 |
| LCS | G ▷ C11×C13 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 143 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#261, C2×D11×D13, D11×D13⋊C3, … |
| maximal normal subgroup of | D11×#261, C2×D11×D13, D11×D13⋊C3, … |
| maximal quotient of | D13×Dic11, D11×Dic13, #11765930, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(572, 7);