Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | Dic3×D5⋊AGL(1,𝔽5) |
| derived, Hall | C3×C52 ⋊ C2×C42 |
| Sylow | C52 ⋊ C2×C4×Dic3 |
| Sylow | C3 ⋊ C4×D5⋊AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D5⋊AGL(1,𝔽5) |
| commutator, hypocenter | C3×C52 | C2×C42 |
| Fitting, socle | C2×C3×C52 | C22×C4 |
| prime radical | C2×C3×D52 | C22 |
| cosocle | C2×C3×C5⋊D5 | C23 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
492 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #72230601, #72230656, C4×D3×D5⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | #72230601, #72230656, C4×D3×D5⋊AGL(1,𝔽5), … |
| maximal quotient of | #72259924 |
Past the SmallGroups library coverage — no SmallGroups id.