Finite Group DatabasebetaFinite Group Databasebeta| order | 18378 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D1021⋊C9 |
| unambiguous semidirect product | (C1021⋊C9)⋊C2 |
| derived, Sylow | C1021 ⋊ C2×C9 |
| Hall | C1021⋊C9 ⋊ C2 |
| Hall | D1021 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D1021⋊C3 |
| commutator, hypocenter | C1021 | C2×C9 |
| Fitting, socle, cosocle | C3×C1021 | C2×C3 |
| prime radical | C3×D1021 | C3 |
| LCS | G ▷ C1021 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9189 |
Polycyclic presentation:
2,3,1021,3|b^3=d,c^a=c^1020,c^b=c^652528 conjugacy classes — view the full character table.
| maximal subgroup of | #16861391⋊C9, C2×D1021⋊C9 |
| maximal normal subgroup of | #16861391⋊C9, C2×D1021⋊C9 |
| maximal quotient of | Dic1021⋊C9, C2×D1021⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18378, 2);