Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C23 · Schur multiplier (H2) = C3 |
| direct product | C5×C23×#4380 |
| Fitting, socle, Hall | C32×C52×C23 ⋊ C4 |
| derived | C32×C5 ⋊ C4×C5×C23 |
| Hall | C52×C23 ⋊ #157 |
| Hall | C32×C52 ⋊ C4×C23 |
| Hall | C32×C23 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C52 ⋊ C23×#157 |
| Sylow | C32 ⋊ C5×AGL(1,𝔽5)×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C23 | #4380 |
| commutator, hypocenter | C32×C5 | C4×C5×C23 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C23 | C4 |
| prime radical | C5×C23×C3⋊D15 | C2 |
| cosocle | C3⋊D15 | C2×C5×C23 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C5×C23 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1380 |
1725 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 253);