Finite Group DatabasebetaFinite Group Databasebeta| order | 26487 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C27 · Schur multiplier (H2) = C33 |
| direct product | C32×#15668887 |
| Fitting, socle | C32×C109 ⋊ C27 |
| derived, Sylow | C109 ⋊ C32×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #15668887 |
| commutator, hypocenter | C109 | C32×C27 |
| Frattini | C1 | G |
| Fitting, socle | C32×C109 | C27 |
| prime radical | C32×C109⋊C3 | C9 |
| cosocle | #11758281 | C33 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C32 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 981 |
279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26487, 372);