Finite Group DatabasebetaFinite Group Databasebeta| order | 21420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D51×C5⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (D35×D51)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C7×C17 | C22×C3 |
| LCS | G ▷ C3×C5×C7×C17 | |
| UCS | C1 | |
176 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1785 |
459 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21420, 218);