Finite Group DatabasebetaFinite Group Databasebeta| order | 18723 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×C79⋊C3 |
| unambiguous semidirect product | C79⋊(C3×C79) |
| Fitting, socle, Sylow | C792 ⋊ C3 |
| derived | C79 ⋊ C3×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | C79⋊C3 |
| commutator, cosocle, hypocenter | C79 | C3×C79 |
| Frattini | C1 | G |
| Fitting, socle | C792 | C3 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C79 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 237 |
2291 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C79×D79⋊C3, (C79⋊C3)⋊D79, D79×C79⋊C3, … |
| maximal normal subgroup of | C79×D79⋊C3, (C79⋊C3)⋊D79, D79×C79⋊C3, … |
| maximal quotient of | C2×C79×C79⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18723, 3);