Finite Group DatabasebetaFinite Group Databasebeta| order | 26588 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C23⋊#11923884 |
| Fitting, socle, derived, Hall | C172×C23 ⋊ C4 |
| Sylow | C172 ⋊ Dic23 |
| Sylow | C23 ⋊ #11923884 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C172×C23 | C4 |
| prime radical, cosocle | C23×C17⋊D17 | C2 |
| LCS | G ▷ C172×C23 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 782 |
Polycyclic presentation:
2^2,17^2,23|a^2=b,c^a=c^13,d^a=d^4,e^a=e^22,c^b=c^16,d^b=d^161682 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26588, 31);