Finite Group DatabasebetaFinite Group Databasebeta| order | 8064 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211 |
| direct product | D7×#10595278 |
| Fitting | C2×C32×C7×D4 ⋊ C23 |
| Hall | C32×C7 ⋊ C22×#120 |
| Sylow | C32 ⋊ C2×D7×#120 |
| Sylow | C7 ⋊ C2×#10595278 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D32×D7 |
| commutator, socle, cosocle | C22×C32×C7 | C25 |
| Fitting | C2×C32×C7×D4 | C23 |
| hypercenter | C2×D4 | D32×D7 |
| hypocenter | C32×C7 | C22×#120 |
| LCS | G ▷ C22×C32×C7 ▷ C32×C7 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
19538 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
330 conjugacy classes. The character table is too large to display.
| maximal quotient of | D7×#11864777 |
Past the SmallGroups library coverage — no SmallGroups id.