Finite Group DatabasebetaFinite Group Databasebeta| order | 23660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C7⋊#16809991 |
| derived, Hall | C5×C7×C132 ⋊ C4 |
| Hall | C7×C132 ⋊ Dic5 |
| Hall | C5×C132 ⋊ Dic7 |
| Sylow | C132 ⋊ Dic35 |
| Hall | C5×C7 ⋊ #10621725 |
| Sylow | C7 ⋊ #16809991 |
| Sylow | C5 ⋊ C7⋊#10621725 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C7⋊(C13⋊D13)) |
| commutator, hypocenter | C5×C7×C132 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C5×C7×C132 | C2 |
| LCS | G ▷ C5×C7×C132 | |
| UCS | C1 ◁ C2 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23660 |
Polycyclic presentation:
2,5,7,13^2,2|a^2=f,b^a=b^4,c^a=c^6,d^a=d^12,e^a=e^125918 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23660, 43);