Finite Group DatabasebetaFinite Group Databasebeta| order | 23660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D35⋊D169 |
| unambiguous semidirect product | D845⋊D7 |
| unambiguous semidirect product | D1183⋊D5 |
| Fitting, derived, Hall | C5×C7×C169 ⋊ C22 |
| Hall | C7×C169 ⋊ C2×D5 |
| Hall | C5×C169 ⋊ C2×D7 |
| Sylow | C169 ⋊ D5×D7 |
| Hall | C5×C7 ⋊ C2×D169 |
| Sylow | C7 ⋊ D5×D169 |
| Sylow | C5 ⋊ D7×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C7×C169 | C22 |
| Frattini | C13 | D35⋊D13 |
| socle | C5×C7×C13 | C2×D13 |
| LCS | G ▷ C5×C7×C169 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5915 |
Polycyclic presentation:
2^2,5,7,13^2|e^13=f^12,d^a=d^6,e^a=e^12f,f^a=f^12,c^b=c^4,d^b=d^61616 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23660, 28);