Finite Group DatabasebetaFinite Group Databasebeta| order | 26910 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D4485 |
| unambiguous semidirect product | C5⋊(C3⋊D897) |
| unambiguous semidirect product | C13⋊(C3⋊D345) |
| unambiguous semidirect product | C23⋊(C3⋊D195) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C13×C23 | C2 |
| LCS | G ▷ C32×C5×C13×C23 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13455 |
Polycyclic presentation:
2,3^2,5,13,23|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^12,f^a=f^226729 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26910, 64);