Finite Group DatabasebetaFinite Group Databasebeta| order | 14400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C22×D32×#1043 |
| Fitting, socle | C22×C32×C52 ⋊ C22×C4 |
| derived, Hall | C32×C52 ⋊ C24×C4 |
| Sylow | C52 ⋊ C22×C4×D32 |
| Sylow | C32 ⋊ C24×#1043 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D32×#1043 |
| commutator, hypocenter | C32×C52 | C24×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C52 | C22×C4 |
| prime radical | C22×D32×C5⋊D5 | C2 |
| cosocle | C32×C5⋊D5 | C25 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C22 | |
22736 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#1043×#3811 |
| maximal normal subgroup of | C2×#1043×#3811 |
| maximal quotient of | C2×#1043×#3811 |
Past the SmallGroups library coverage — no SmallGroups id.