Finite Group DatabasebetaFinite Group Databasebeta| order | 26187 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×#22576609 |
| Fitting, socle, Hall | C3×C29×C43 ⋊ C7 |
| derived, Hall | C29×C43 ⋊ C3×C7 |
| Hall | C3×C43 ⋊ C29⋊C7 |
| Hall | C3×C29 ⋊ C43⋊C7 |
| Sylow | C43 ⋊ C3×C29⋊C7 |
| Sylow | C29 ⋊ C3×C43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #22576609 |
| commutator, cosocle, hypocenter | C29×C43 | C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C43 | C7 |
| LCS | G ▷ C29×C43 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3741 |
555 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26187, 8);