Finite Group DatabasebetaFinite Group Databasebeta| order | 3584 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C212×C4 |
| direct product | D7×#15258 |
| Fitting | C7×#15258 ⋊ C2 |
| Sylow | C7 ⋊ C2×#15258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C24×D7 |
| commutator, socle, cosocle | C24×C7 | C25 |
| Fitting | C7×#15258 | C2 |
| hypercenter | #15258 | D7 |
| hypocenter | C7 | C2×#15258 |
| LCS | G ▷ C24×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ #15258 | |
43692 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
290 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.