Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | C4×#6057⋊C3 |
| Fitting | C4×C52 ⋊ SL(2,𝔽3) |
| derived | #6057 ⋊ C3×C4 |
| Hall | C4×#6057 ⋊ C3 |
| Sylow | C52 ⋊ C4×SL(2,𝔽3) |
75 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
32 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#72209598, C4×((D5⋊AGL(1,𝔽5))⋊C2)⋊C3 |
| maximal normal subgroup of | C4×((D5⋊AGL(1,𝔽5))⋊C2)⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.