Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#24925058 |
| derived, Sylow | C337 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #19129199 |
| commutator, hypocenter | C337 | C2×C32 |
| Frattini | C2 | C2×#19129199 |
| Fitting, socle, prime radical | C22×C337 | C16 |
| cosocle | #19129197 | C22 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C22 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21568 |
148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1677);