Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×C23⋊#1042 |
| unambiguous semidirect product | C23⋊(C32×#1042) |
| Fitting, socle, Hall | C32×C52×C23 ⋊ C4 |
| derived, Hall | C52×C23 ⋊ C32×C4 |
| Hall | C32×C52 ⋊ Dic23 |
| Hall | C32×C23 ⋊ #1042 |
| Sylow | C52 ⋊ C32×Dic23 |
| Sylow | C23 ⋊ C32×#1042 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C23⋊#1042 |
| commutator, hypocenter | C52×C23 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C23 | C4 |
| prime radical | C32×C5×D5×C23 | C2 |
| cosocle | C5×D5×C23 | C2×C32 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 ◁ C32 | |
156 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, 267);