Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C43 |
| direct product | C42×#13062438 |
| Fitting | C42×C337 ⋊ C4 |
| derived, Sylow | C337 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #13062438 |
| commutator, hypocenter | C337 | C43 |
| Frattini | C22 | C22×#13062438 |
| Fitting | C42×C337 | C4 |
| socle | C22×C337 | C22×C4 |
| prime radical, cosocle | C22×D337 | C23 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C42 | |
258 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, 1483);