Finite Group DatabasebetaFinite Group Databasebeta| order | 21350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D2135 |
| unambiguous semidirect product | C5⋊(C5×D427) |
| unambiguous semidirect product | C7⋊(C5×D305) |
| Fitting, socle, Hall | C52×C7×C61 ⋊ C2 |
| derived | C5×C7×C61 ⋊ C2×C5 |
| Hall | C52×C61 ⋊ D7 |
| Hall | C7×C61 ⋊ C5×D5 |
| Hall | C52×C7 ⋊ D61 |
| Sylow | C61 ⋊ C5×D35 |
| Sylow | C52 ⋊ D427 |
| Sylow | C7 ⋊ C5×D305 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D2135 |
| commutator, cosocle, hypocenter | C5×C7×C61 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C61 | C2 |
| LCS | G ▷ C5×C7×C61 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4270 |
5345 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21350, 28);