Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×#19129199 |
| Fitting | C4×C337 ⋊ C16 |
| derived, Sylow | C337 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #19129199 |
| commutator, hypocenter | C337 | C4×C16 |
| Frattini | C2 | C2×#19129199 |
| Fitting | C4×C337 | C16 |
| socle | C2×C337 | C2×C16 |
| prime radical | C2×D337 | C2×C8 |
| cosocle | C2×#14582115 | C22 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C4 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1348 |
148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1674);