Finite Group DatabasebetaFinite Group Databasebeta| order | 21300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | Dic3×C71⋊C25 |
| unambiguous semidirect product | C3⋊(C4×C71⋊C25) |
| unambiguous semidirect product | (Dic3×C71)⋊C25 |
| derived, Hall | C3×C71 ⋊ C4×C25 |
| Hall | C3×C71⋊C25 ⋊ C4 |
| Hall | Dic3×C71 ⋊ C25 |
| Sylow | C71 ⋊ Dic3×C25 |
| Sylow | C3 ⋊ C4×C71⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C5 | D3×C71⋊C5 |
| commutator, hypocenter | C3×C71 | C4×C25 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C71 | C2×C5 |
| LCS | G ▷ C3×C71 | |
| UCS | C1 ◁ C2×C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21300 |
570 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21300, 11);