Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×#10597182 |
| Fitting, socle | C23×C3×C52 ⋊ C2×C4 |
| derived, Hall | C3×C52 ⋊ C24×C4 |
| Sylow | C52 ⋊ C23×C4×D3 |
| Sylow | C3 ⋊ C23×D5⋊AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #10597182 |
| commutator, hypocenter | C3×C52 | C24×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C52 | C2×C4 |
| prime radical | C23×D15⋊D5 | C2 |
| cosocle | C3×C5⋊D5 | C25 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C23 | |
5920 conjugacy classes of subgroups; only the 997 normal subgroups are shown.
This group has 5920 conjugacy classes of subgroups — too many to draw. Only its 997 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
192 conjugacy classes — view the full character table.
| maximal quotient of | #72260362 |
Past the SmallGroups library coverage — no SmallGroups id.