Finite Group DatabasebetaFinite Group Databasebeta| order | 18723 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C6241⋊C3 |
| Fitting, derived, Sylow | C6241 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C6241 | C3 |
| Frattini, socle | C79 | C79⋊C3 |
| LCS | G ▷ C6241 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6241 |
Polycyclic presentation:
3,79^2|b^79=c,b^a=b^23c^57,c^a=c^232083 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D6241⋊C3, C2×C6241⋊C3 |
| maximal normal subgroup of | D6241⋊C3, C2×C6241⋊C3 |
| maximal quotient of | C2×C6241⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18723, 1);