Finite Group DatabasebetaFinite Group Databasebeta| order | 18174 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C13⋊C3)⋊D233 |
| unambiguous semidirect product | C233⋊(D13⋊C3) |
| unambiguous semidirect product | D3029⋊C3 |
| Fitting, socle, derived, Hall | C13×C233 ⋊ C2×C3 |
| Hall | C13⋊C3×C233 ⋊ C2 |
| Hall | D3029 ⋊ C3 |
| Sylow | C233 ⋊ D13⋊C3 |
| Hall | C13⋊C3 ⋊ D233 |
| Sylow | C13 ⋊ C3×D233 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C233 | C2×C3 |
| LCS | G ▷ C13×C233 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3029 |
Polycyclic presentation:
2,3,13,233|c^a=c^12,d^a=d^232,c^b=c^3820 conjugacy classes — view the full character table.
| maximal subgroup of | #27131125⋊C3, #27131126⋊C3, D13⋊C3×D233, … |
| maximal normal subgroup of | #27131125⋊C3, #27131126⋊C3, D13⋊C3×D233, … |
| maximal quotient of | Dic3029⋊C3, C2×(C13⋊C3)⋊D233 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18174, 12);