Finite Group DatabasebetaFinite Group Databasebeta| order | 26558 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C271 · Schur multiplier (H2) = C1 |
| direct product | D49×C271 |
| unambiguous semidirect product | C49⋊(C2×C271) |
| Fitting, Hall | C49×C271 ⋊ C2 |
| derived, Sylow | C49 ⋊ C2×C271 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C271 | D49 |
| commutator, cosocle, hypocenter | C49 | C2×C271 |
| Frattini | C7 | D7×C271 |
| Fitting | C49×C271 | C2 |
| socle | C7×C271 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C271 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13279 |
7046 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26558, 2);