Finite Group DatabasebetaFinite Group Databasebeta| order | 26065 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C401⋊C5 |
| unambiguous semidirect product | C401⋊(C5×C13) |
| unambiguous semidirect product | (C13×C401)⋊C5 |
| Fitting, socle, Hall | C13×C401 ⋊ C5 |
| derived, Sylow | C401 ⋊ C5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C401⋊C5 |
| commutator, cosocle, hypocenter | C401 | C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C401 | C5 |
| LCS | G ▷ C401 | |
| UCS | C1 ◁ C13 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5213 |
1105 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26065, 1);