Finite Group DatabasebetaFinite Group Databasebeta| order | 14400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210×C3 |
| direct product | C23×C3⋊D3×#1043 |
| Fitting, socle | C23×C32×C52 ⋊ C2×C4 |
| derived, Hall | C32×C52 ⋊ C24×C4 |
| Sylow | C52 ⋊ C23×C4×C3⋊D3 |
| Sylow | C32 ⋊ C24×#1043 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊D3×#1043 |
| commutator, hypocenter | C32×C52 | C24×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C32×C52 | C2×C4 |
| prime radical | C23×C3⋊D3×C5⋊D5 | C2 |
| cosocle | C32×C5⋊D5 | C25 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C23 | |
32688 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1800 |
480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4×C3⋊D3×#1043, C2×#1043×#3811, C2×C3⋊D3×#11717375 |
| maximal normal subgroup of | C2×D4×C3⋊D3×#1043, C2×#1043×#3811, C2×C3⋊D3×#11717375 |
| maximal quotient of | C2×D4×C3⋊D3×#1043 |
Past the SmallGroups library coverage — no SmallGroups id.