Finite Group DatabasebetaFinite Group Databasebeta| order | 4014 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D223⋊C9 |
| unambiguous semidirect product | (C223⋊C9)⋊C2 |
| derived, Sylow | C223 ⋊ C2×C9 |
| Hall | C223⋊C9 ⋊ C2 |
| Hall | D223 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D223⋊C3 |
| commutator, hypocenter | C223 | C2×C9 |
| Fitting, socle, cosocle | C3×C223 | C2×C3 |
| prime radical | C3×D223 | C3 |
| LCS | G ▷ C223 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 232 |
| transitive degree | μt(G) = 2007 |
Polycyclic presentation:
2,3,223,3|b^3=d,c^a=c^222,c^b=c^183129 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D223⋊C9, C5⋊(D223⋊C9), C7×D223⋊C9, … |
| maximal normal subgroup of | C5×D223⋊C9, C7×D223⋊C9 |
| maximal quotient of | C5×D223⋊C9, C5⋊(D223⋊C9), C7×D223⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4014, 2);