Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×(C5⋊D5)⋊D23 |
| unambiguous semidirect product | D115⋊(C32×D5) |
| Fitting, socle, Hall | C32×C52×C23 ⋊ C22 |
| derived, Hall | C52×C23 ⋊ C22×C32 |
| Hall | C32×C52 ⋊ C2×D23 |
| Hall | C32×C23 ⋊ D52 |
| Sylow | C52 ⋊ C2×C32×D23 |
| Sylow | C23 ⋊ C32×D52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | (C5⋊D5)⋊D23 |
| commutator, cosocle, hypocenter | C52×C23 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C23 | C22 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 ◁ C32 | |
288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2070 |
1530 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 270);