Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C23×#14582115 |
| Fitting, socle | C23×C337 ⋊ C8 |
| derived, Sylow | C337 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #14582115 |
| commutator, hypocenter | C337 | C23×C8 |
| Frattini | C1 | G |
| Fitting, socle | C23×C337 | C8 |
| prime radical | C23×D337 | C4 |
| cosocle | #13062438 | C24 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C23 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2696 |
400 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1672);