Finite Group DatabasebetaFinite Group Databasebeta| order | 19323 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C113 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C19×C113 ⋊ C3 |
| derived, Sylow | C19 ⋊ C32×C113 |
| Hall | C19×C113 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C113 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C32×C113 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C113 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C113 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6441 |
3051 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C113×D19⋊C3, C3×(C19⋊C3)⋊D113, C3×C19⋊C3×D113, … |
| maximal normal subgroup of | C3×C113×D19⋊C3, C3×(C19⋊C3)⋊D113, C3×C19⋊C3×D113, … |
| maximal quotient of | C2×C3×C19⋊C3×C113 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19323, 5);