Finite Group DatabasebetaFinite Group Databasebeta| order | 19293 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×C109⋊C3 |
| unambiguous semidirect product | C109⋊(C3×C59) |
| unambiguous semidirect product | (C59×C109)⋊C3 |
| Fitting, socle, Hall | C59×C109 ⋊ C3 |
| derived, Sylow | C109 ⋊ C3×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | C109⋊C3 |
| commutator, cosocle, hypocenter | C109 | C3×C59 |
| Frattini | C1 | G |
| Fitting, socle | C59×C109 | C3 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C59 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6431 |
2301 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C59×C109⋊C3, C59×D109⋊C3, D59×C109⋊C3, … |
| maximal normal subgroup of | C2×C59×C109⋊C3, C59×D109⋊C3, D59×C109⋊C3, … |
| maximal quotient of | C2×C59×C109⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19293, 1);