Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D1348 |
| Fitting | C23×C4×C337 ⋊ C2 |
| Sylow | C337 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D337 |
| commutator, cosocle | C2×C337 | C25 |
| Frattini | C2 | C24×D337 |
| Fitting | C23×C4×C337 | C2 |
| socle | C24×C337 | C22 |
| hypercenter | C23×C4 | D337 |
| hypocenter | C337 | C23×D4 |
| LCS | G ▷ C2×C337 ▷ C337 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
1362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10784 |
5416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1371);