Finite Group DatabasebetaFinite Group Databasebeta| order | 26588 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#11923876 |
| Fitting, derived, Hall | C23×C289 ⋊ C4 |
| Sylow | C289 ⋊ Dic23 |
| Sylow | C23 ⋊ #11923876 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C23×C289 | C4 |
| Frattini | C17 | C23⋊#595 |
| socle | C17×C23 | #595 |
| prime radical, cosocle | C23×D289 | C2 |
| LCS | G ▷ C23×C289 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6647 |
Polycyclic presentation:
2^2,17,23,17|a^2=b,c^17=e^11,c^a=c^13e,d^a=d^22,e^a=e^13,c^b=c^16e^6,e^b=e^161682 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26588, 7);