Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C162 · Schur multiplier (H2) = C16 |
| direct product | C16×C83⋊C16 |
| unambiguous semidirect product | C83⋊C162 |
| derived, Sylow | C83 ⋊ C162 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8×C16 | D83 |
| commutator, hypocenter | C83 | C162 |
| Frattini | C82 | C2×D83 |
| Fitting | C8×C16×C83 | C2 |
| socle, prime radical | C22×C83 | C82 |
| cosocle | C82×C83 | C22 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C8×C16 | |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21248 |
5504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 56181);