Finite Group DatabasebetaFinite Group Databasebeta| order | 26550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C59 · Schur multiplier (H2) = C5 |
| direct product | C2×C59×C52⋊C9 |
| unambiguous semidirect product | (C2×C52)⋊(C9×C59) |
| unambiguous semidirect product | (C2×C52×C59)⋊C9 |
| derived, Sylow | C52 ⋊ C2×C9×C59 |
| Hall | C2×C52×C59 ⋊ C9 |
| Hall | C52×C59 ⋊ C2×C9 |
| Hall | C2×C52 ⋊ C9×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C59 | C52⋊C3 |
| commutator, hypocenter | C52 | C2×C9×C59 |
| Frattini | C3 | C2×C59×C52⋊C3 |
| Fitting, socle, prime radical | C2×C3×C52×C59 | C3 |
| cosocle | C3×C52 | C2×C3×C59 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C3×C59 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5310 |
3894 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26550, 27);