Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×C23⋊#1042 |
| unambiguous semidirect product | C23⋊(C9×#1042) |
| Fitting, Hall | C52×C9×C23 ⋊ C4 |
| derived, Hall | C52×C23 ⋊ C4×C9 |
| Hall | C52×C9 ⋊ Dic23 |
| Hall | C9×C23 ⋊ #1042 |
| Sylow | C52 ⋊ C9×Dic23 |
| Sylow | C23 ⋊ C9×#1042 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C23⋊#1042 |
| commutator, hypocenter | C52×C23 | C4×C9 |
| Frattini | C3 | C3×C23⋊#1042 |
| Fitting | C52×C9×C23 | C4 |
| socle | C3×C52×C23 | C3×C4 |
| prime radical, cosocle | C3×C5×D5×C23 | C2×C3 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 ◁ C9 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4140 |
2097 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 130);