Finite Group DatabasebetaFinite Group Databasebeta| order | 26015 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×C121⋊C5 |
| unambiguous semidirect product | C121⋊(C5×C43) |
| unambiguous semidirect product | (C43×C121)⋊C5 |
| Fitting, Hall | C43×C121 ⋊ C5 |
| derived, Sylow | C121 ⋊ C5×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | C121⋊C5 |
| commutator, cosocle, hypocenter | C121 | C5×C43 |
| Frattini | C11 | C43×C11⋊C5 |
| Fitting | C43×C121 | C5 |
| socle | C11×C43 | C11⋊C5 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C43 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5203 |
1247 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26015, 2);