Finite Group DatabasebetaFinite Group Databasebeta| order | 23940 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×D7×D95 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D7×D95 |
| commutator, hypocenter | C5×C7×C19 | C22×C9 |
| Frattini | C3 | C3×D7×D95 |
| Fitting | C5×C7×C9×C19 | C22 |
| socle, cosocle | C3×C5×C7×C19 | C22×C3 |
| prime radical | C3×D7×D95 | C3 |
| LCS | G ▷ C5×C7×C19 | |
| UCS | C1 ◁ C9 | |
120 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5985 |
2205 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23940, 130);