Finite Group DatabasebetaFinite Group Databasebeta| order | 26550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| direct product | D59×C52⋊C9 |
| unambiguous semidirect product | C59⋊(C2×C52⋊C9) |
| unambiguous semidirect product | (C52×D59)⋊C9 |
| derived, Hall | C52×C59 ⋊ C2×C9 |
| Hall | C59×C52⋊C9 ⋊ C2 |
| Hall | C52×D59 ⋊ C9 |
| Sylow | C59 ⋊ C2×C52⋊C9 |
| Sylow | C52 ⋊ C9×D59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C52⋊C3×D59 |
| commutator, hypocenter | C52×C59 | C2×C9 |
| Fitting, socle, cosocle | C3×C52×C59 | C2×C3 |
| prime radical | C3×C52×D59 | C3 |
| LCS | G ▷ C52×C59 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2655 |
1023 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26550, 26);