Finite Group DatabasebetaFinite Group Databasebeta| order | 23940 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊AGL(1,𝔽19))⋊D7 |
| unambiguous semidirect product | (#4296⋊D7)⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C19 | C22×C9 |
| prime radical | (C5⋊(D19⋊C3))⋊D7 | C3 |
| cosocle | C5×C7×C19⋊C3 | C22×C3 |
| LCS | G ▷ C5×C7×C19 | |
| UCS | C1 | |
120 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 665 |
Polycyclic presentation:
2^2,3^2,5,7,19|c^3=d,f^a=f^6,g^a=g^18,e^b=e^4,f^b=f^6,g^c=g^4,g^d=g^7199 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23940, 352);