Finite Group DatabasebetaFinite Group Databasebeta| order | 21018 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C31⋊C3)⋊D113 |
| unambiguous semidirect product | C113⋊(D31⋊C3) |
| unambiguous semidirect product | D3503⋊C3 |
| Fitting, socle, derived, Hall | C31×C113 ⋊ C2×C3 |
| Hall | C31⋊C3×C113 ⋊ C2 |
| Hall | D3503 ⋊ C3 |
| Sylow | C113 ⋊ D31⋊C3 |
| Hall | C31⋊C3 ⋊ D113 |
| Sylow | C31 ⋊ C3×D113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C113 | C2×C3 |
| LCS | G ▷ C31×C113 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3503 |
Polycyclic presentation:
2,3,31,113|c^a=c^30,d^a=d^112,c^b=c^25739 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21018, 12);