Finite Group DatabasebetaFinite Group Databasebeta| order | 9720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D5×(#4207⋊C2)⋊C3 |
| Fitting, Hall | C5×3−1+4 ⋊ C23 |
| derived | C5×#737 ⋊ C23×C3 |
| Sylow | 3−1+4 ⋊ C22×D5 |
| Sylow | C5 ⋊ C2×(#4207⋊C2)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×#737 | C23×C3 |
| Frattini | C3 | C3×D5×#1113 |
| Fitting | C5×3−1+4 | C23 |
| socle | C3×C5 | C2×C3×#1113 |
| LCS | G ▷ C5×#737 | |
| UCS | C1 | |
1184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
188 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×(#4207⋊C2)⋊C3 |
| maximal normal subgroup of | AGL(1,𝔽5)×(#4207⋊C2)⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.