Finite Group DatabasebetaFinite Group Databasebeta| order | 26588 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C23⋊#11923880 |
| derived, Hall | C172×C23 ⋊ C4 |
| Sylow | C172 ⋊ Dic23 |
| Sylow | C23 ⋊ #11923880 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C17⋊D391 |
| commutator, hypocenter | C172×C23 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C172×C23 | C2 |
| LCS | G ▷ C172×C23 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26588 |
Polycyclic presentation:
2,17^2,23,2|a^2=e,b^a=b^16,c^a=c^16,d^a=d^226650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26588, 13);