Finite Group DatabasebetaFinite Group Databasebeta| order | 23660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C7⋊#16810007 |
| Fitting, socle, derived, Hall | C5×C7×C132 ⋊ C4 |
| Hall | C7×C132 ⋊ AGL(1,𝔽5) |
| Hall | C5×C132 ⋊ Dic7 |
| Sylow | C132 ⋊ C7⋊AGL(1,𝔽5) |
| Hall | C5×C7 ⋊ #10621725 |
| Sylow | C7 ⋊ #16810007 |
| Sylow | C5 ⋊ C7⋊#10621725 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C132 | C4 |
| prime radical, cosocle | C7×D5×C132 | C2 |
| LCS | G ▷ C5×C7×C132 | |
| UCS | C1 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5915 |
Polycyclic presentation:
2^2,5,7,13^2|a^2=b,c^a=c^2,d^a=d^6,e^a=e^12,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, 105);