Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D3×D5⋊AGL(1,𝔽5) |
| Fitting, socle | C2×C3×C52 ⋊ C22×C4 |
| derived, Hall | C3×C52 ⋊ C23×C4 |
| Sylow | C52 ⋊ C22×C4×D3 |
| Sylow | C3 ⋊ C22×D5⋊AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×D5⋊AGL(1,𝔽5) |
| commutator, hypocenter | C3×C52 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52 | C22×C4 |
| prime radical | C2×D3×D52 | C2 |
| cosocle | C3×C5⋊D5 | C24 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
1052 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 194 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
84 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.