Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C5 |
| direct product | C11×C5⋊D245 |
| unambiguous semidirect product | C5⋊(C11×D245) |
| unambiguous semidirect product | C49⋊(C11×C5⋊D5) |
| Fitting, Hall | C52×C11×C49 ⋊ C2 |
| derived, Hall | C52×C49 ⋊ C2×C11 |
| Hall | C11×C49 ⋊ C5⋊D5 |
| Hall | C52×C11 ⋊ D49 |
| Sylow | C49 ⋊ C11×C5⋊D5 |
| Sylow | C52 ⋊ C11×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C5⋊D245 |
| commutator, cosocle, hypocenter | C52×C49 | C2×C11 |
| Frattini | C7 | C11×C5⋊D35 |
| Fitting | C52×C11×C49 | C2 |
| socle | C52×C7×C11 | D7 |
| LCS | G ▷ C52×C49 | |
| UCS | C1 ◁ C11 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13475 |
6754 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 31);