Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3×C5 |
| direct product | C2×C3⋊(C3⋊(C5⋊D115)) |
| unambiguous semidirect product | (C2×C3)⋊(C3⋊(C5⋊D115)) |
| unambiguous semidirect product | (C2×C5)⋊(C3⋊D345) |
| unambiguous semidirect product | (C2×C23)⋊(C3⋊(C3⋊(C5⋊D5))) |
| Fitting, socle | C2×C32×C52×C23 ⋊ C2 |
| derived, Hall | C32×C52×C23 ⋊ C22 |
| Hall | C52×C23 ⋊ C2×C3⋊D3 |
| Hall | C32×C52 ⋊ C2×D23 |
| Hall | C32×C23 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ C2×C3⋊D69 |
| Sylow | C23 ⋊ C2×C3⋊(C3⋊(C5⋊D5)) |
| Sylow | C32 ⋊ C2×C5⋊D115 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(C3⋊(C5⋊D115)) |
| commutator, cosocle, hypocenter | C32×C52×C23 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C52×C23 | C2 |
| LCS | G ▷ C32×C52×C23 | |
| UCS | C1 ◁ C2 | |
480 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10350 |
5178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 371);