Finite Group DatabasebetaFinite Group Databasebeta| order | 21420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊(C17⋊AGL(1,𝔽7)) |
| unambiguous semidirect product | (D15⋊D119)⋊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 40 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1785 |
Polycyclic presentation:
2^2,3^2,5,7,17|e^a=e^4,f^a=f^6,g^a=g^16,d^b=d^2,e^b=e^4,f^c=f^2405 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21420, 224);