Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C22×D5×A5 |
| Fitting | C22×C5 ⋊ C2×A5 |
| socle | C22×C5×A5 ⋊ C2 |
| derived | C5×A5 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×A5 |
| commutator, hypocenter | C5×A5 | C23 |
| Frattini | C1 | G |
| Fitting | C22×C5 | C2×A5 |
| socle | C22×C5×A5 | C2 |
| cosocle | C5 | C23×A5 |
| LCS | G ▷ C5×A5 | |
| UCS | C1 ◁ C22 | |
656 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
80 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C3×D5×A5, C22×A52, C22×A5⋊AGL(1,𝔽5) |
| maximal normal subgroup of | C22×C3×D5×A5, C22×A5⋊AGL(1,𝔽5) |
| maximal quotient of | C2×D5×#6732, C22×C3×D5×A5 |
Past the SmallGroups library coverage — no SmallGroups id.