Finite Group DatabasebetaFinite Group Databasebeta| order | 26850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D537 |
| unambiguous semidirect product | C3⋊(C52×D179) |
| unambiguous semidirect product | C179⋊(C52×D3) |
| Fitting, socle, Hall | C3×C52×C179 ⋊ C2 |
| derived, Hall | C3×C179 ⋊ C2×C52 |
| Hall | C52×C179 ⋊ D3 |
| Sylow | C179 ⋊ C52×D3 |
| Hall | C3×C52 ⋊ D179 |
| Sylow | C3 ⋊ C52×D179 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D537 |
| commutator, cosocle, hypocenter | C3×C179 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C179 | C2 |
| LCS | G ▷ C3×C179 | |
| UCS | C1 ◁ C52 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13425 |
6750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26850, 22);