Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×C3×D5⋊AGL(1,𝔽5) |
| Fitting, socle | C23×C3×C52 ⋊ C2×C4 |
| derived, Sylow | C52 ⋊ C24×C3×C4 |
| Hall | C3×C52 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3 | D5⋊AGL(1,𝔽5) |
| commutator, hypocenter | C52 | C24×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C52 | C2×C4 |
| prime radical | C23×C3×D52 | C2 |
| cosocle | C5⋊D5 | C25×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C23×C3 | |
5920 conjugacy classes of subgroups; only the 1662 normal subgroups are shown.
This group has 5920 conjugacy classes of subgroups — too many to draw. Only its 1662 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
336 conjugacy classes. The character table is too large to display.
| maximal quotient of | C3×#72213412 |
Past the SmallGroups library coverage — no SmallGroups id.