Finite Group DatabasebetaFinite Group Databasebeta| order | 18126 |
| isoclinism | isoclinic class of C3⋊(D19⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C53 · Schur multiplier (H2) = C1 |
| Fitting, socle | C3×C19×C53 ⋊ C2×C3 |
| derived | C3×C19 ⋊ C2×C3×C53 |
| Hall | C3×C53×C19⋊C3 ⋊ C2 |
| Hall | C19×C53 ⋊ C3×D3 |
| Hall | C3×C19⋊C3 ⋊ C2×C53 |
| Sylow | C19 ⋊ C3×D3×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | C3⋊(D19⋊C3) |
| commutator, cosocle, hypocenter | C3×C19 | C2×C3×C53 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C53 | C2×C3 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C53 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3021 |
954 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18126, 21);