Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C23⋊(#1039⋊C9) |
| unambiguous semidirect product | (C23⋊#1039)⋊C9 |
| derived, Hall | C52×C23 ⋊ C4×C9 |
| Hall | C23×C52⋊C9 ⋊ C4 |
| Hall | C23⋊#1039 ⋊ C9 |
| Hall | C52⋊C9 ⋊ Dic23 |
| Sylow | C52 ⋊ C9×Dic23 |
| Sylow | C23 ⋊ #1039⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C23⋊((C5⋊D5)⋊C3) |
| commutator, hypocenter | C52×C23 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C52×C23 | C2×C3 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 ◁ C2×C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4140 |
Polycyclic presentation:
2,3,5^2,23,2,3|a^2=f,b^3=g,c^a=c^4,d^a=d^4,e^a=e^22,c^b=cd,d^b=c^2d^3786 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 45);