Finite Group DatabasebetaFinite Group Databasebeta| order | 26005 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C743⋊C7 |
| unambiguous semidirect product | C743⋊(C5×C7) |
| unambiguous semidirect product | (C5×C743)⋊C7 |
| Fitting, socle, Hall | C5×C743 ⋊ C7 |
| derived, Sylow | C743 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C743⋊C7 |
| commutator, cosocle, hypocenter | C743 | C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C743 | C7 |
| LCS | G ▷ C743 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3715 |
565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26005, 1);