Finite Group DatabasebetaFinite Group Databasebeta| order | 23660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#16809979 |
| Fitting, derived, Hall | C5×C7×C169 ⋊ C4 |
| Hall | C7×C169 ⋊ AGL(1,𝔽5) |
| Hall | C5×C169 ⋊ Dic7 |
| Sylow | C169 ⋊ C7⋊AGL(1,𝔽5) |
| Hall | C5×C7 ⋊ Dic169 |
| Sylow | C7 ⋊ #16809979 |
| Sylow | C5 ⋊ Dic1183 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C7×C169 | C4 |
| Frattini | C13 | C7⋊#63120 |
| socle | C5×C7×C13 | Dic13 |
| prime radical | C7×D5×C13 | D13 |
| cosocle | C7×D5×C169 | C2 |
| LCS | G ▷ C5×C7×C169 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5915 |
Polycyclic presentation:
2^2,5,7,13^2|a^2=b,e^13=f^12,c^a=c^2,d^a=d^6,e^a=e^12f,f^a=f^12,c^b=c^42369 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23660, 19);