Finite Group DatabasebetaFinite Group Databasebeta| order | 20754 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #23780650⋊C2 |
| derived, Sylow | C1153 ⋊ C2×C9 |
| Hall | #23780650 ⋊ C2 |
| Hall | D1153 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D1153⋊C3 |
| commutator, hypocenter | C1153 | C2×C9 |
| Fitting, socle, cosocle | C3×C1153 | C2×C3 |
| prime radical | C3×D1153 | C3 |
| LCS | G ▷ C1153 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10377 |
Polycyclic presentation:
2,3,1153,3|b^3=d,c^a=c^1152,c^b=c^650594 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20754, 2);