Finite Group DatabasebetaFinite Group Databasebeta| order | 18639 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C19×C109 ⋊ C32 |
| Sylow | C109 ⋊ C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×C109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C109 | C32 |
| LCS | G ▷ C19×C109 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2071 |
351 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C19⋊C3)⋊(D109⋊C3), D19⋊C3×C109⋊C3, C19⋊C3×D109⋊C3, … |
| maximal normal subgroup of | (C19⋊C3)⋊(D109⋊C3), D19⋊C3×C109⋊C3, C19⋊C3×D109⋊C3, … |
| maximal quotient of | C2×C19⋊C3×C109⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18639, 19);