Finite Group DatabasebetaFinite Group Databasebeta| order | 21350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C61 · Schur multiplier (H2) = C1 |
| direct product | C7×D25×C61 |
| unambiguous semidirect product | C25⋊(C2×C7×C61) |
| Fitting, Hall | C7×C25×C61 ⋊ C2 |
| derived, Sylow | C25 ⋊ C2×C7×C61 |
| Hall | C25×C61 ⋊ C2×C7 |
| Hall | C7×C25 ⋊ C2×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C61 | D25 |
| commutator, cosocle, hypocenter | C25 | C2×C7×C61 |
| Frattini | C5 | C7×D5×C61 |
| Fitting | C7×C25×C61 | C2 |
| socle | C5×C7×C61 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C7×C61 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10675 |
5978 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21350, 6);