Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#11717479 |
| Fitting | C3×C52×D4 ⋊ C22 |
| Hall | C3×C52 ⋊ H(5,𝔽2) |
| Sylow | C52 ⋊ C3×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C22×D52 |
| commutator, cosocle | C2×C52 | C24×C3 |
| Frattini | C2 | C22×C3×D52 |
| Fitting | C3×C52×D4 | C22 |
| socle | C2×C3×C52 | C24 |
| hypercenter | C3×D4 | D52 |
| hypocenter | C52 | C3×H(5,𝔽2) |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C3 ◁ C3×D4 | |
772 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
231 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13107821 |
| maximal normal subgroup of | C3×#13107821 |
Past the SmallGroups library coverage — no SmallGroups id.