Finite Group DatabasebetaFinite Group Databasebeta| order | 21420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D51⋊D105 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C7×C17 | C22 |
| LCS | G ▷ C32×C5×C7×C17 | |
| UCS | C1 | |
176 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3570 |
Polycyclic presentation:
2^2,3^2,5,7,17|d^a=d^2,g^a=g^16,c^b=c^2,d^b=d^2,e^b=e^4,f^b=f^61434 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21420, 340);