Finite Group DatabasebetaFinite Group Databasebeta| order | 1081 |
| isoclinism | isoclinic class of C47⋊C23 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊C23 |
| Fitting, socle, derived, Sylow | C47 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C47 | C23 |
| LCS | G ▷ C47 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 47 |
Polycyclic presentation:
23,47|b^a=b^2525 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽47), C2×C47⋊C23, C3×C47⋊C23, … |
| maximal normal subgroup of | AGL(1,𝔽47), C2×C47⋊C23, C3×C47⋊C23, … |
| maximal quotient of | C2×C47⋊C23, C3×C47⋊C23, C11×C47⋊C23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1081, 1);