Finite Group DatabasebetaFinite Group Databasebeta| order | 26816 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×C419⋊C8 |
| unambiguous semidirect product | C419⋊C82 |
| derived, Sylow | C419 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D419 |
| commutator, hypocenter | C419 | C82 |
| Frattini | C42 | C2×D419 |
| Fitting | C4×C8×C419 | C2 |
| socle, prime radical | C22×C419 | C42 |
| cosocle | C42×C419 | C22 |
| LCS | G ▷ C419 | |
| UCS | C1 ◁ C4×C8 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26816 |
6752 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26816, 269);