Finite Group DatabasebetaFinite Group Databasebeta| order | 23660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16810010⋊C7 |
| Fitting, socle, derived, Hall | C5×C132 ⋊ C4×C7 |
| Hall | C5×C132⋊C7 ⋊ C4 |
| Hall | #16810010 ⋊ C7 |
| Hall | C132⋊C7 ⋊ Dic5 |
| Sylow | C132 ⋊ C7×Dic5 |
| Sylow | C5 ⋊ #10621728⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C132 | C4×C7 |
| prime radical | C5×(C13⋊D13)⋊C7 | C2 |
| cosocle | C5×C13⋊D13 | C2×C7 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 455 |
Polycyclic presentation:
2,7,2,5,13^2|a^2=c,d^a=d^4,e^a=e^5,f^a=f^5,e^b=e^7f^7,f^b=ef^3,e^c=e^12,f^c=f^1286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23660, 69);