Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×#13062438 |
| unambiguous semidirect product | D337⋊(C23×C4) |
| Fitting, socle | C24×C337 ⋊ C4 |
| derived, Sylow | C337 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | #13062438 |
| commutator, hypocenter | C337 | C24×C4 |
| Frattini | C1 | G |
| Fitting, socle | C24×C337 | C4 |
| prime radical | C24×D337 | C2 |
| cosocle | D337 | C25 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C24 | |
1362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5392 |
1408 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1630);